While technically true, the term has been largely co-opted by the A/V realm. It’s pretty rare to hear outside of the context.
To be clear the codec implements the compression (or other encoding) algorithm. So when talking about codec's we mean the implementation. But when talking about the algorithm, we are talking about the standard of encoding the encoder or decoder implements.
No, rare in general.
It's a layman's co-opting, and laymen outnumber specialists in every field.