There's a big difference between sailing clubs, charter ownership and time-share arrangements.
Sailing clubs are just that, clubs. They might have a clubhouse, some boats, a marina and/or moorings, completely depending on their goals. Those that do own boats are sometimes set up around that fleet or are a mix of owner boats and fleet boats for classes and one-design racing. Where I am there are 4 clubs within a mile set up around J/24s or Colgate 26s. Two are businesses that allow members to borrow the boats when they aren't used for classes, one is a non-profit in the same situation and one is a proper club. The businesses tend to be more restrictive on boat use (day use only, no overnights, limited guests, skippers must take other members is the boat isn't full), but require little to no initiation fee.
Charter ownerships allow you to own the boat and they operate it as a charter. You can take it basically take it whenever you want, with a notice period. There are financial incentives to limit your time, so if you have it for extended periods, you might need to pay the charter firm something. I've also heard of situations where the charter company will charge a nominal fee and give you any boat they have available. In my opinion, this works great if you want 4 weeks or so per year and would be chartering anyway. The math I've seen shows you take on a lion's share of the risk, but get cheap chartering in nice places (BVIs, Turkey, etc.).
The last are time shares, aka fractional ownership. They work somewhere between the club and the charter ownership. You typically get the boat on shorter periods than a charter, for example a day or weekend, and are targeted at people near the harbor.
There are a variety of options in each of these. The club I used to race with had a clubhouse and marina, no boats and a great membership. Another club I've spent time with owns mooring balls, operates races, holds classes, owns a small fleet of J/24s and has a great clubhouse. Yet another was a straight business run by the owner who basically sold lessons and let the "members" (who had no voting rights or responsibilities) use the boats when classes weren't on.
I'm not really into the charter ownership thing. I've loaned my boat to others, including the previous owner, and it rarely turns out to be an equitable or fun experience. I like knowing where my gear is, what's broken, why it's broken and what stupid thing I did to break it.