Thanks for writing this, I think we are all guilty at times of merging the meanings of these two words.
Just wondering which side of the fence you'd place Facebook Groups? Many of them, even the very biggest, seem to be very trivial indeed and I doubt most people could name more than a few of the ones they have signed up to.
But more seriously, Facebook seems to have a lot of biggish groups that have a clear focus but still this doesn't translate to any real action. For example in the UK the BBC is consulting on the closure of one of its smaller radio stations 6Music. The FB group very quickly got into six figures but the number of people who had visited the BBC's official consultation site to make comments was stuck at about 5% of the FB group membership.
FB seems to be a place for expressing very casual opinions which makes the Like button seem a little suspect.