"speaking in many tongues" and the like usually are from a Biblical context, else Russian язык practically always translates into "language"

They can be used interchangeably, when used in the sense of a spoken language. But “language” is much more common, and tongue is more literary. Also, “language” can be used in broader senses, like “the language of art” or “the language of love” — which means words or actions that people use to express artistic or romantic ideas. “Tongue” would never be used in these phrases.

Thanks a lot for your contribution.

Are they used interchangeably? No, not really. Do they always overlap? Again no, not really. In my experience tongue, in reference to language tends to be used in an elevated way as part of expressions: mother tongue = first language.