Colloquially they are synonyms. Especially amongst people who don't make software. It's not derogatory and not worth getting bent out of shape about.
BUT ... (Bet you saw this coming)
Coders turn detailed specs into code. No real thought required.
Programmers, or software developers, design systems and code them themselves.
That's the distinction I make anyway. I've seen coders at some workplaces. It's a dreary job and I would never do it.