[Mithadan]

Welcome to the Barrow-Downs, JeyEn! An excellent first post!

I believe that Huinesoron, has this issue analyzed correctly. It is troubling that Gandalf believed that Bilbo's find was "a Great Ring, as plainly it was - that at least was clear from the first." I will add to Huisesoron's post by noting that Gandalf, at best, only believed that Sauron had either gathered the Seven or that they had been destroyed. So, having overlooked that only the One was unadorned and without a stone, he may have believed that it was one of the Seven. And he had been assured by Saruman that the One was lost permanently; that it had found its way to the sea. Even so, he concedes that it is perilous for a mortal to possess any of the Rings of Power.

I could go out on a limb and theorize that there was a distinction between, first, the lesser rings, second, the Great Rings, and third, Rings of Power, but this would be a stretch. Gandalf states "But the Great Rings, the Rings of Power, they were perilous." This seems to clearly mean that there is no distinction between the Great Rings and the Rings of Power.