I don't know how other LUGs in North America and Europe define themselves, but for us at QuéLUG (for Quebec LEGO User Group, and yes, we do use the term LUG even if the official language of our association is French), a LUG is much more than just "a meeting of LEGO fans of a particular area".
For us, QuéLUG is more like a fan club, an association of fans of LEGO from all over Quebec. And just like any other organized association, QuéLUG has a democratic structure (we have a President, a Board of Directors and we hold a general assembly every year), written rules (which were voted by the general assembly of members) and official membership (along with fees and priviledges).
Yes, we do organize meetings in person at least 4 times a year (the dates are even planned ahead in our rules), but we also organize group buys, drafts, contests with prizes and public displays with local event organizers. We even have our very own website and forum to discuss LEGO news, share our MOCs and share information on local LEGO sales.
But that's only one point of view. When we founded QuéLUG in 2006, we looked at other associations of AFOLs around the world (FreeLUG among others) and took what we thought fitted us best. We went with an official structure and official rules because we wanted an organized association from the start. It was kind of a pain at first (imagine: a Board of Directors of 3 members for an association of 10 members!), but it paid off in the long run, because as the membership grew, we didn't have to put those structures in place in order to keep things running smoothly.
But that's what fitted us best. An informal club with no particular rules, no membership fees and fewer activities is just fine for other AFOLs, and that's OK. Anyway, overall, it's just another excuse to indulge even more in our passion for the small ABS bricks...