Careful translators recognize that the articular construction of the noun points to an identity, a personality, whereas a singular anarthrous predicate noun preceding the verb points to a quality about someone. Therefore, John’s statement that the Word or Logos was “a god” or “divine” or “godlike” does not mean that he was the God with whom he was. It merely expresses a certain quality about the Word, or Logos, but it does not identify him as one and the same as God himself (Rbi8, 1579).
The 10/15/93 WT (pp. 27-28) clarifies this statement even more:
The New World Translation, correctly viewing the word “God” as indefinite, as well as bringing out the qualitative aspect indicated by the Greek structure, uses the indefinite article in English: “The Word was a god.”
So Witnesses say QEOS in John 1:1c has both indefinite and qualitative semantic force: the Word is a god or divine being. One difference, however, is that Witnesses employ the adnominal "divine" in its weaker sense, whereas Trinitarians utilize "divine" with a stronger sense or meaning, so that it only applies to God (compare the AT at 1:1c). Professor Dale Tuggy helpfully has made distinctions between the strong and weak sense of "divine" in his work on the Trinity doctrine. I highly recommend his analyses.
Another difference is that while Trinitarians like Richard A. Young or Daniel B. Wallace are inclined to view QEOS in Jn 1:1c as a "monadic" or one-of-a-kind noun, Jehovah's Witnesses evidently believe QEOS is a count noun since we encounter the plural QEOI in both the LXX and NT with no indication that the writers in these particular instances are using the nominal QEOS pejoratively (Ps 8:4-5).
Now it's a well-known fact that Trinitarians make the afirmation, "Jesus is God." But one nagging logical difficulty that I think attends the Trinitarian proposition "Jesus is God" is that Trinitarians seem forced to view the Father, Son and Holy Spirit as "relatively identical" with the Godhead (i.e., God). Yet those who study identity in a non-theological context have pointed out that "relative identity" appears to be a sketchy concept. A logician named Peter Geach developed a sophisticated argument for relative identity that Richard Cartwright and other logicians aptly tried to refute, and did refute IMO.
Some elementary principles of logic are that A = A, identity relations are transitive, and identity is absolute/necessary:
(1) Cicero is Tully.
(2) Water is H20.
(3) Heat is the motion of molecules/atoms.
(4) Hesperus is Phosphorus.
(5) 2 + 2 = 4.
Leibniz' law also comes into play here and says that if X and Y commonly exemplify all properties, then X and Y are identical. The converse of this statement is that if X and Y are identical, then X and Y commonly exemplify all properties. That is why Cicero (X) is said to be identical with Y (Tully), KAI TO LOIPON. 2 + 2 = 4 is also a statement of identity.
But Trinitarians are saying none of the above when they assert that "Jesus is God." Rather, the proposition "Jesus is God" only claims that the Son of God is relatively identical with the Godhead, according to Geach and others. The Trinitarian proposition is thus akin to the assertions: "Aristotle is rational" or "Socrates is wise."