Like Jack I attended (ONCE) what was advertised as 'A Session' .
I arrived and saw that I had met the guy running it before . I asked him if it WAS a session , or a Singaround . Definately a session was his reply . The First performer put a capo on fret One of his guitar , and did a quite tasty rendition of an American Contempory song in C Shapes ! C BLOODY SHARP as a session tune ?? As a Singaround it was not upleasant , but a session it most definately was not .
I agree that 'Session' on its own would indicate Tunes , while 'Singaround' is fairly obvious .
'Mixed Session' or 'Open Sesion' would both indicate tunes AND songs , with participation being part of the mix ! .
There is a VERY Good Mixed session in The New Tavern in Sidmouth for the entirety of the Festival , by the way