I don't feel any need to get hung up on terminology: suffice it to say that to me, "a session" is anywhere any number of singers and/or musicians get together to sing and/or play tunes or both. If you need to describe it to others, you can call it "instrumental", "singing" or "mixed songs and tunes".
As an aside to this, my 2 offspring, (when they were teenagers), fell about laughing when I said I was "off for a session". It obviously had some totally different meaning in their peer group!