Classical harmonies do allow unisons and octaves.

Bluegrass harmonies generally have lead, tenor and baritone parts, often parallel, and should not have unisons or octaves. When a bass vocal part is added, usually for acapella gospel tunes, the bass part may duplicate one of the other parts an octave lower.

Folks who sing bluegrass regularly, often can wing the tenor or baritone part. The tenor part is a third above the lead line and the baritone part is a 4th below (or sometimes a fifth above, called a high baritone). The terms tenor and baritone do not indicate range, but the relationship to the lead line.