My lowest note to sing is F2 (as baritone lowest) but my highest note is C5 (a tenors highest). So What am I classified as? Cause I'm both?
Singers are not classified according to the pitch of noise they can create but according to the range people actually are able to enjoy hearing from them. That range tends to be more constrained. Training can extend it to cover most of the accessible range. In case this exceeds the tessitura of a particular fach, one may have the liberty of making a choice based on personal preference. However, much of the time the choice will be made by the audience for professional singers.