What are the specific names for clauses following a comma, dash and such punctuation marks?

Do the clauses which follow a dash, colon, open bracket, and such punctuation marks have specific names other than just being a clause?

Examples of what I mean with the "C"s representing the clauses in question:

1. xxxxxx – CCCCCC – xxxxxxx.
2. xxxxxxxx xxxxxxx – CCCCCC.
3. xxxxxxxx xxxxxxxx: CCCCCC.
4. xxxxxxxx (CCCCCC) xxxxxxx.

Are they all just called clauses? Or does each example have specific name to indicate that they follow a certain punctuation mark?