Distinction between Created Son and Begotten Son for Jehovah's Witnesses In the New Testament, the Greek word monogenēs (μονογενής) appears 9 times and is translated as only or only begotten every time.  4 times it is used to describe the solitary physical descendant of a human being (Luke 7:12, 8:42, 9:38, and Hebrews 11:17).  The other 5 times it is used to describe Jesus as the only begotten Son of God (John 1:14, 1:18, 3:16, 3:18, and 1 John 4:9).  The emphasis appears consistent each time:  That which is begotten is of the same nature as that which begat it.

In Luke's Gospel (3:38) the lineage of Jesus is traced back to Adam, the Son of God.  Since we know from Genesis that Adam was formed by God from the dust of the Earth and that Adam was of a different nature than God who formed him, and since there does not appear to be any record in Scripture of a begotten child that is different in nature from it's begetting parent, we have what appears to be a critical distinction between a begotten son and a created son.


  “We don't use the words begetting or begotten much in modern English,
  but everyone still knows what they mean. To beget is to become the
  father of: to create is to make. And the difference is this. When you
  beget, you beget something of the same kind as yourself. A man begets
  human babies, a beaver begets little beavers and a bird begets eggs
  which turn into little birds. But when you make, you make something of
  a different kind from yourself. A bird makes a nest, a beaver builds a
  dam, a man makes a wireless set – or he may make something more like
  himself than a wireless set: say, a statue. If he is a clever enough
  carver he may make a statue which is very like man indeed. But, of
  course, it is not a real man; it only looks like one. It cannot
  breathe or think. It is not alive.
  
  Now that is the first thing to get clear. What God begets is God; just
  as what man begets is man. What God creates is not God; just as what
  man makes is not man. That is why men are not Son's of God in the
  sense that Christ is. They may be like God in certain ways, but they
  are not things of the same kind. They are more like statues or
  pictures of God.” - C.S. Lewis (Mere Christianity)


Begetting is the father's role.  A child is born of it's mother and begotten of it's father.  Both impart the essential nature of it's parent.  In this way Jesus was human being (through Mary the mother) and Divine being (through God the Father).  Unlike an elephant and an ostrich, which cannot produce offspring because the essential natures are incompatible, humanity (Mary) and Spirit (God) are compatible.  If the son of God was created by God then he certainly was not Divine, but if he was begotten of God then he certainly was.

My question is:  Do Jehovah's Witnesses recognize this distinction between the only begotten Son of God and a created son? If not, how do they explain the consistent use of the term and, if so, how can they then affirm that Jesus was God's first creation since he is so clearly portrayed as begotten not made which then makes him of the same nature as God?
Yes Jehovah’s Witnesses distinguish between Jesus’ unique one of a kind preeminent status and all other sons of God both heavenly and earthly.


  The Greek word mo·no·ge·nesʹ is defined by lexicographers as “single of its kind, only,” or “the only member of a kin or kind.” (Thayer’s Greek-English Lexicon of the New Testament, 1889, p. 417; Liddell and Scott’s Greek-English Lexicon, Oxford, 1968, p. 1144) 


Only begotten Son of God only applies to the one of a kind unique Jesus Christ the only entity created with no agency or instrumentality by Jehovah alone. 
 All other created Sons of God, angelic and human, are Jehovah’s creation made through this unique,one of a kind, only begotten Son of the eternally existing Creator Jehovah.

This puts Jesus in a class by himself. That fits very well with the description (monongenes)

The created  “Sons of God” both angelic and human share a commonality, namely they came into existence through the only begotten Jesus. They thus are not one of a kind, or unique (monongenes).

Your contention that Jesus cannot be both created (ktiʹzo) and begotten (monongenes) is not accurate in our exegesis since the distinction is made between the one and only (monongenes) entity brought into existence (kti’zo) solely by the Eternally existing Creator Jehovah and the entirety of all other beings created by Jehovah through Jesus and for Jesus. Col 1:16 

Now on the claim that monongenes also incorporates the idea of same substance or same nature I am not familiar with that concept. I am aware that the Greek word homoousia came onto the scene at the behest of Constantine during his efforts to unify his Christian subjects. It is not a biblical Greek term but has philosophical Greek roots. 

Jehovah’s Witnesses obviously disagree with the idea that Jesus is eternal like his father. That is out of sync with a claim of same nature or substance I think. He is not Almighty God as is his Father. He is not the Creator Jehovah is. 

A comprehensive collection of JW beliefs in regard to the trinity doctrine can be found in this brochure  

JW take on the phrase “only-begotten” and related items can be found here.

And a similar writing on “creation” can be found here