The bass range is classically E2 to E4, two octaves from the lowest E commonly written in vocal music up to the E above middle C. The signature isn't the top, it's the bottom. A true bass can sustain E2 with full, resonant tone, not a breathy fade or a vocal-fry approximation. If your bottom thins out around F2 or G2, you're a bass-baritone or baritone, not a bass.
The classical bass subtypes: (1) Basso profondo, the deepest, with reliable production down to C2 or lower, repertoire like Sarastro in The Magic Flute. (2) Basso cantante / lyric bass, agile and lighter, range E2-E4, repertoire like Don Giovanni's commendatore. (3) Bass-baritone: sits between bass and baritone, often with bass's depth but baritone's upper extension, range A2-G4.
Pop and rock have very few true basses because contemporary production places vocals in the upper-tenor range to cut through the mix. The bass voices that do appear (Johnny Cash, Leonard Cohen, Barry White) are valued precisely because they're rare. If you're a true bass, embracing the voice type rather than chasing tenor repertoire is a faster path to any kind of public performance.