Clans are groups of up to 20 players. They are formed to compete in the annual clan championship which is determined by the greatest net points. They also compete in clan leagues which, iirc, is set up like the football leagues (promotion, relegation, etc). Some clans skip the competitions and concentrate on their area of mutual interest (music, sports, religion, etc) within the clan's private forum. All clan members should be subscribers, but it doesn't work that way in practice. You can be in 4 clans at the same time, I think, including 1 you are the clanmeister of.
Clubs are open to all members of RHP, subscriber or not. They often have areas of interest they specialize in and many host intera-club touraments. There is no limit to how many people can be in a club. You can be in any number of clubs.