Replies may vary according to the side of the Pond they come from.

In the UK, Open Mic implies a microphone and PA system, and involves the performer going up to the front of the room, possibly on to a stage of some sort, to perform. There may be an MC or someone deciding who performs and for how long. For some reason most of these acts will be solo men with guitars, but that's just my observation, not a rule.

A singaround (I think "song circle" in the US is similar), by contrast,usually means that people sit in a something-like-circular arrangement, perhaps informally at tables, and each person sings in turn, around the room (or not, if they just want to listen). So a singaround is generally less formal and more inclusive, with all the good and bad that this entails. Many singarounds are mostly or entirely unaccompanied.

A session is less formal still, and may be only instrumental, or a mix of tunes and songs. It's often in a public bar with a lot of background noise. In most sessions there are no real rules about who starts a tune or song - you just wait for a suitable opportunity and go for it. People generally join in if they know the tune, or sometimes even if they don't. There isn't usually a PA system, and the guy who brings his own and drowns everyone out is not popular.

There has been lots of discussion in previous threads about the varying expectations and etiquettes of these gatherings, but that's a brief explanation of the main differences as I understand them. I'm sure others will add to this.