Why is John distinguishing God's word (logos) from Jesus who IS God's word/logos become flesh?
Different contexts require different wordings. E.g, Jesus is referred to as "Lamb" in
Then I saw a Lamb, looking as if it had been slain, standing at the center of the throne, encircled by the four living creatures and the elders. The Lamb had seven horns and seven eyes, which are the seven spirits of God sent out into all the earth.
The Greek λόγος has a very wide range of meanings.
Thayer's Greek Lexicon broadly divides the 3 categories of meanings:
I. As respects speech
II. Its use as respects the mind
III. In several passages in the writings of John ὁ λόγος denotes the essential Word of God, i. e. the personal (hypostatic) wisdom and power in union with God, his minister in the creation and government of the universe, the cause of all the world's life both physical and ethical, which for the procurement of man's salvation put on human nature in the person of Jesus the Messiah and shone forth conspicuously from his words and deeds
Thayer lists about a dozen different nuances in the 1st category and six in the 2nd.
It would seem that God's word/logos is not an exclusive term that applies only to Jesus.
True. In fact, most of the time it does not refer to Jesus' person. Only John uses it that way in Thayer's 3rd category.
Are there different forms or expressions of logos - only one of which is Jesus who is the fleshly human expression of God's word?
No, according to Thayer's Greek Lexicon.