Hi Thespionage
A folk Group for me means a small group of musicians who primarily play/sing to entertain others and of course themselves adn are likely to have enough material to do two forty minute spots combining original and 'traditional' material in some recognised genre.
A Folk club, again, in my opinion, allows anyone to sing or play usually 2/3 numbers maximum. I can't speak for the US, but in UK such clubs generally have a number of informal and formalised codes of practice which may/may not appeal to everyone.

A session is generally considerd to be a group of people who play music predominantly generally with a thematic approach, Irish, Northumbrian, Appalachian or whatever.

A further alternative is just have an open meeting and go round the room asking for a contribution from everyone.

If you are starting off something to attract people Beetle cat has the right idea. Advertise it, find a decent venue, which has a good atmosphere (good ale etc) and act as the MC. It will soon find its own level.
Good luck mate - I hope its a success.