I'm not entirely au fait with nomenclature, but I think what we do is kind of a singaround with instruments.

Great ones may happen spontaneously, but if you run a regular one it can take a surprising amount of discreet work to keep it running smoothly.

Things which contribute to a positive experience.

1) Courtesy:
* Making sure your instrument is in tune (if tunable)
* Acknowledging everyone's contribution with applause, a nod, a murmur or whatever
* Not tuning up loudly or talking loudly while other participants are singing/playing
* Not stopping the person who called/started the tune or song after 8 bars because that's not the version you know, so are they sure they're doing it right?
* Not jumping in out of turn because you just thought of a good one
* Sitting a song out if you don't know the song or are not confident of being able to play along without ruining it for the person taking their turn

2) Discipline - no iron fist, just preventing chaos
* Not widdling loudly between songs, or "practising [loudly] until the next song starts"
* Tuning up, finding your capo and any lyrics or music you need before your turn arrives.
* Offering to pass on your turn if you can't get your arse in gear promptly
* Not starting songs that you will have to abandon halfway through because you are not prepared.

Technical ability is not the most important thing, IMHO. As has been observed, many people can't sing "well", but their performances are enjoyable, nonetheless.

We have a chap at our session who doesn't play guitar well or sing well, but his attitude is spot-on and we're all rooting for him. He actually does the Father Ted thing... "Wait, wait - I can get this bit!" KERRANG! It all adds to the atmosphere and the fun.

If a session/singaround takes place in a pub I would suggest that it is considerate of the MC to have at least some aspirations to entertain the other punters who may be present in addition to members of the session. Some of my points above - the widdling and playing half a song, for example - are made with this in mind.