Index To All Six Sections
Part I: Definition and Historical Background, Relying On Others To Decide What We Should Believe
Part II - Plurality in The Godhead
Part III - The Deity of Christ & The Deity of The Holy Spirit
Part IV: Passages That Supposedly "Prove" the Trinity.
Part V: The Grammar... Can it legitimately be used to support the idea that the Holy Spirit is the third Person of the Trinity
Part VI: The Holy Spirit... a Separate Person, Or The Divine Presence And Power Of The Father Himself
Part VII: The doctrine of the trinity that has remained virtually unchanged to this day found its roots in paganism not the Bible. This largely due to the part played by the Cappadocian Fathers - three ancient Greek philosophers and mystics.
You Are Here Part VIII: The Son is "begotten" of the Father, and the Spirit "proceeds" from the Father. A difference yes, but not what The Cappadocian Fathers made it out to be
Part IX: Summary and Conclusion
The Son Is Begotten And The Spirit Proceeds
Historian and Christian theologian Alister E. McGrath, President of the Oxford Centre for Christian Apologetics and Professor of Divinity at Gresham College in London says (All Emphasis Added)
Although the Cappadocian writers stress that they do not accept that either the Son or Spirit is subordinate to the Father, they nevertheless explicitly state that the Father is to be regarded as the source or fountainhead of the Trinity. The being of the Father is imparted to both the Son and the Spirit, although in different ways: the Son is "begotten" of the Father, and the Spirit "proceeds" from the Father. Gregory of Nyssa thus writes of "the one person of the Father, from whom the Son is begotten and the Spirit proceeds" ...
These two terms are intended to express the idea that both Son and spirit derive from the father, but are derived in different ways. The vocabulary is clumsy, reflecting the fact that the Greek words involved are difficult to translate into modern English... An obvious question arises here: why should the Cappadocian fathers, and other Greek writers, spend so much time and effort on distinguishing Son and Spirit in this way? The answer is important. A failure to distinguish the ways in which Son and Spirit derive from the one and the same Father would lead to go on having two sons, which would have raised insurmountable problems. 
So are both the Son and Spirit derived from the Father in "different ways"?
To repeat something I have said many times before ... At some point in time, we really need to stop blindly accepting theories and explanations put forth by others and do our own research. While the vast majority of us have no knowledge of Hebrew or Greek, modern software programs and Interlinear Bibles have allowed us not only to examine the meaning of precise words in the Scriptures but, by tracing every occurrence, see how it is used in other passages. There is no question that the study is time consuming and although it certainly wont make you an expert, very often it serves to confirm or disprove what you may have been told, read etc.
In this case, when the New Testament says "the Son is begotten and the Spirit proceeds" it uses two separate Greek words. If we take a look at the original words used by the authors of the Gospels .we do we will find that Gregory of Nyssa neglected to mention that Jesus also spoke of 'proceeding' or 'coming from' the Father.
When Jesus told the disciples that the Holy Spirit proceeds from the Father, He used the Greek word ekporeuetai
When the Helper comes, whom I will send to you from the Father, that is the Spirit of truth who proceeds from (Gk. ekporeuetai) the Father, He will testify about Me, (John 15:26 NASB) Source
However, this verb is in no way exclusive to the Holy Spirit. The exact form is used, both literally and figuratively, of all manner of things that come out of something else. For example,
But this kind (of demon) does not go out (Gk. ekporeuetai) except by prayer and fasting." (Matthew 17:21 NASB)
because it does not go into his heart, but into his stomach, and is eliminated (Gk. ekporeuetai) " (Mark 7:19 NASB)
And if anyone wants to harm them, fire flows out (Gk. ekporeuetai) of their mouth and devours their enemies; so if anyone wants to harm them, he must be killed in this way. (Revelation 11:5 NASB)
From His mouth comes (Gk. ekporeuetai) a sharp sword, so that with it He may strike down the nations, and He will rule them with a rod of iron; and He treads the wine press of the fierce wrath of God, the Almighty. (Revelation 19:15 NASB) Source
Exelthon (1st person singular)
Although He used a different verb, on two separate occasions Jesus told believing Jews that He had "come forth" from the Father.
Jesus said to them, "If God were your Father, you would love Me, for I proceeded forth (Gk. exelthon.) and have come from God, for I have not even come on My own initiative, but He sent (Gr. apostello) Me. (John 8:42 NASB)
for the Father Himself loves you, because you have loved Me and have believed that I came forth (Gk. exelthon. 1st person singular) from the Father. "I came forth (Gk. exelthon. 1st person singular) from the Father and have come into the world; I am leaving the world again and going to the Father." His disciples *said, "Lo, now You are speaking plainly and are not using a figure of speech. "Now we know that You know all things, and have no need for anyone to question You; by this we believe that You came from (Gk. exelthes. 2nd person singular) God. " (John 16:27-30 NASB)
Once again the Greek verb is in no way exclusive to the Savior but is used in a variety of different situations in the New Testament
"Then the kingdom of heaven will be comparable to ten virgins, who took their lamps and went out (Gk. exelthon) to meet the bridegroom. (Matthew 25:1 NASB)
The Pharisees came out (Gk. exelthon) and began to argue with Him, seeking from Him a sign from heaven, to test Him. (Mark 8:11 NASB)
You yourselves also know, Philippians, that at the first preaching of the gospel, after I left (Gk. exelthon) Macedonia, no church shared with me in the matter of giving and receiving but you alone; (Philippians 4:15 NASB)
and the seven angels who had the seven plagues came out (Gk. exelthon) of the temple, clothed in linen, clean and bright, and girded around their chests with golden sashes. (Revelation 15:6 NASB)
Note: that John 16:28-30 also uses the Greek word apesteilen which means to send out (properly on a mission). In other words, Jesus was saying two things - 1.) He proceeded from and 2.) was "sent by" the Father. Source
Is There Any Difference Between Ekporeuetai and Exelthon?
There seems to be absolutely no difference in the practical use of either verb. Both are used in the sense of traveling from a point of origin, including physically emerging from something... be it a city, a building, the earth, or someone's body.
That fact that both verbs say exactly the same thing is clearly seen in the story of a demon possessed boy related in Matthew 17.
In verse 18, Jesus used the Greek verb exelthen, which is the same verb He used when He told the disciples that He Himself came forth from the Father (John 16:28-30)
And Jesus rebuked him, and the demon came out (Gk. exelthen) of him, and the boy was cured at once. (Matthew 17:18 NASB)
But just a couple of verses later, Jesus used ekporeuetai the verb He used in John 15:26 when He told the disciples that the Holy Spirit proceeds from the Father
Additional evidence is found in the fact that Matthew and Luke each used one of the two verbs in exactly the same situation.
This news spread (Gk. exelthen) throughout all that land. (Matthew 9:26 NASB)
And the report about Him was spreading (Gk. exeporeueto.) into every locality in the surrounding district. (Luke 4:37 NASB)
The Son is "Begotten" of the Father
Gregory of Nyssa wrote "the one person of the Father, from whom the Son is begotten and the Spirit proceeds" ...
There is no question that when the Bible says the Son was begotten, it is referring to His earthly birth. The Greek word monogenes (single of its kind, only) is used in most verses that concern the incarnation,
And the Word became flesh, and dwelt among us, and we saw His glory, glory as of the only begotten (Gk. monogenes) from the Father, full of grace and truth... No one has seen God at any time; the only begotten (Gk. monogenes) God who is in the bosom of the Father, He has explained Him. (John 1:14, 18 NASB)
"For God so loved the world, that He gave His only begotten (Gk. monogenés) Son, that whoever believes in Him shall not perish, but have eternal life...He who believes in Him is not judged; he who does not believe has been judged already, because he has not believed in the name of the only begotten (Gk. monogenés) Son of God (John 3:16, 18 NASB)
Monogenes was used of Abraham's son Isaac.
By faith Abraham, when he was tested, offered up Isaac, and he who had received the promises was offering up his only begotten (Gk. monogeneé) son; (Hebrews 11:17 NASB)
Luke records two separate incidents when the parent of an only child who was ill begged Jesus for help, and another occasion when Jesus brought to life the only son of a widow
Now as He approached the gate of the city, a dead man was being carried out, the only son of his mother, and she was a widow; and a sizeable crowd from the city was with her. (Luke 7:12 NASB)
for he had an only daughter, about twelve years old, and she was dying. But as He went, the crowds were pressing against Him. (Luke 8:42 NASB)
And a man from the crowd shouted, saying, "Teacher, I beg You to look at my son, for he is my only boy, (Luke 9:38 NASB)
However, although there may have been a particular point in time when Jesus proceeded from the Father, He too was from everlasting. He and the Father have always been.
The Cappadocian fathers wrote that Jesus and the Holy Spirit derive from the Father in "different" ways, i.e. "the Son is begotten and the Spirit proceeds". However, Jesus Himself twice said He had "come forth" from the Father and 'begotten' was only used of physical birth.
Alister E. McGrath wrote that
A failure to distinguish the ways in which Son and Spirit derive from the one and the same Father would lead to go on having two sons, which would have raised insurmountable problems. 
A correct and Scriptural understanding of the nature of the Holy Spirit (rather than theories based on Greek philosophy amply supported by the occult) makes this absolutely irrelevant. The Holy Spirit is the Spirit of God Himself and Christ is called a "Son" because in His earthly incarnation, He was "begotten" of the Father.
In any case, even if the Holy Spirit were a separate third person of the trinity Jesus would have had two Fathers. He Himself said God was his father as did Luke however, Matthew tells us that Jesus was conceived by the Holy Spirit.
that God has fulfilled this promise to our children in that He raised up Jesus, as it is also written in the second Psalm, 'You are My Son; today I have begotten (Gk. gennao) You.' (Acts 13:33 NASB)
But when he had considered this, behold, an angel of the Lord appeared to him in a dream, saying, "Joseph, son of David, do not be afraid to take Mary as your wife; for the Child who has been conceived (Gk. gennao) in her is of the Holy Spirit. (Matthew 1:20 NASB)
Continue On To Part IX - Summary and Conclusion. The church, substituting their own rules for what the Scriptures teach, has often insisted you believe in their version of the trinity in order to consider yourself as being saved. The truth is that how many Beings the Godhead consists of has absolutely no bearing on salvation. We are no closer to really understanding everything about the Father and the spiritual realm than we are to taking a stroll around Pluto. HERE
 Alister E. McGrath. Historical Theology: An Introduction to the History of Christian Thought. Wiley-Blackwell; 2 edition (July 23, 2012) Paperback. Pg. 57, 61