Whenever acids & bases are mentioned, they're usually the Bronsted-Lowry type (H
+ donors & acceptors). You might also hear about Lewis acids & bases, which involve donors/acceptors of electrons instead of H
+, but these will be refered to as "Lewis acids" or "Lewis bases" (or often in organic chemistry, "electrophiles" & "nucleophiles") rather than simply "acids" or "bases" (unless your chemistry teacher or textbook happens to be fiendishly ambiguous
).
Anions of strong acids--like HSO
4-, Cl
- & NO
3---won't accept H
+, at least not to any significant degree. So, not all negative ions will act as a (Bronsted-Lowry) base.