I sometimes choose “queer” to describe my identity. As others have said, it's an umbrella term that can cover any non-straight orientation, and it's a handy word for people like me who aren’t confident in their orientation. “Queer” conveys that I'm not straight without exacting my sexuality, which I prefer not to define precisely.
“Gay” is generally a more specific term. It usually means attraction solely to members of one's gender. I have heard “gay” used casually as a self-descriptor by bi/pan folks, but this is a divisive usage. Some people support using “gay” as an umbrella term, while others see it as the erasure of bisexual, pansexual, and other non-homo or heterosexual orientations.
The distinction between them is of little importance until someone wishes to be identified as one or the other, in which case this person's preferred term should be used.