Tenor, bass, baritone refer to the range in which a singing part is. In barbershop, where it's all male or all female, the tenor is the highest voice, lead and baritone are about the same range (baritone sings harmony and lead sings melody), and bass is the lowest range. The ranges overlap of course, and in a particular spot in the song the bass part may be higher than the baritone, but overall, the parts are based on ranges.
In mixed groups, it goes, in order of highest to lowest: soprano, alto, tenor, baritone, bass. Soprano, alto, and tenor can be sung by women, tenor, baritone, bass by men. Some choir directors won't have female tenors in their groups because the tone is different, but it is within the range for women with deeper voices. And some individuals have greater range than that - I'm generalizing.
Within the parts, a particular song may have first soprano, second soprano, etc, again referring to range - first being higher range.
And a particular individual may have a range that allows them to sing different parts. Before transition, I could've sung second soprano, alto, or tenor, although I was more comfortable in alto or tenor. Post-transition, I can sing baritone or bass, and some tenor parts, although probably not as high as barbershop tenor parts. Baritone or bass one (which is the higher bass) is my most comfortable range.
If it helps to place where the tenor range is, most male pop singers sing in a tenor range.
Dennis