After thinking about it, and Jeff's post, there should be few questions about spoken or written languages (most, if not all, would be off-topic for too localized) here. As such, it seems like languages is the best tag for the site.
Agree, most people use them synonymously anyway. And there seems slight confusion. In a context with internationalization the usage as natural language would make sense, like in this question. But they could (and most likely should) use internationalization. In addition there is natural-language and spoken-languages. Maybe some text in the tag wiki would help users to make the distinction.
I don't think on a site titled "programmers" we necessarily should disambiguate language.
All tags start with the assumption that they are most relevant to the audience of that site.
I think languages (the plural form) is generally better but I strongly feel that adding "programming-" to tags is highly redundant on a site by, and for, programmers...