I kinda lean toward Hagh's take in post #3. I think of a "band" as a group that has a catalog (30-40 songs) they can play well enough to qualify as entertainment (?). Personally, I enjoy a good jam (groups & gangs) but not endless 12 bar blues ... jamming on "covers" but taking whatever liberties you want to get through the song. Usually produces plenty of oops and smiling cringes but it's all for fun (usually just an excuse to drink beer :)... and is considerably less stressful than preparing songs for public consumption.
Keep at it Kasp - play with any/every - gang/group you can ... practice diligently... and eventually the personnel for a "band" will emerge.