different designers, what do they do?

[insignificantly]

i never really understood what different designers do. you have level design, character design, etc.
when someone asks me what i want to be as a profession, i answer, game designer.
but reading interviews and posts on different sites i'm beginning to doubt that i know what a game designer is.

is a game designer, any designer that works on a game? so are character and level designers also game designers?

i always thought a game designer was the guy that gets the idea for the gameplay, and designs it, and the controlls, etc. and that a level designer designs the levels, which is a whole other profession. and that the lead designer is a game designer that leads all the other game designers and other designers.

but on different sites i found that alot of people say that a game designer is any designer and lead designer is the gameplay desiger (or something).

does the word game designer even have 1 meaning, or is it an opinion what the word means?

thanks.