I do both. They're interchangeable.
Actually, I use the term "believer" more I do either Baptist or Christian.
Believer is more precise, to me. If I describe myself as Baptist, I could be one of 38 kinds. But at least people have an idea what I believe. The label Christian means everything from born-again, to Roman Catholic, to Mormon to Christian Science. All it tells them is that I'm not an atheist, Muslim or Hindu.
My favorite self-label is "Right-wing, redneck, deep-water Baptist." One time, I used that description of myself, and the one I was talking with said, "Oh, one of those." He thought I meant IFB. I told him I was SBC, and SBCers could be one one of those, too.
Christian is who who has Jesus as their Lord and saviour...
the"label"idenifies us as to which Christian 'group" we agree with on doctrines
Such as baptist/methodist/presby etc
Christian is the 'term" we oroginally ALL got labeled with, and that was before any baptist Churches were started!