"What if it is both a musician's session and welcomes songs?"

In that case list it as what you wish, The aim is not to differentiate between folk singers and folk musicians but simply to accept that there is a difference between an event where individuals get up to entertain the rest of the room, be it a singaround or a guest night and an event where musicians turn up with their instrument and play as part of a group on just about every tune of the night.

Easiest way is to look at other people's listings, and put yours where you feel it fits best.

All the best

Jim Hancock