The term flying club means (to me, at least) a large partnership in which a bunch of pilots share ownership of one or more planes, and establish some set of rules for sharing usage, establish ways of generating income (some combination of monthly dues and hourly flying rates) that pay the expenses, typically run the club with volunteer effort by the members, and are organized to serve the needs of the membership, not to generate profit. In this model, the members own the planes; legal structures may be established such that the flying club, as its own entity, actually owns the plane, but the effect is the same. It's also possible, of course, for a flying club to arrange a lease of a plane instead of ownership, or some other kind of arrangement.
In such an equity-based flying club, the rules established by the members are very likely to differ from those typical at a flight school. One significant difference is that flight schools are mostly about training, so it's a problem for them if you take a plane a way for a week, and it's sitting idle as you sit idle on the beach. In a flying club, the members set the rules to conform with their preferences, and they're likely to be certificated pilots for whom one of the uses of a plane is to actually go places, and so they establish rules friendly to this.
The term "flying club", however, is also used to describe a marketing plan of a for-profit business, one that typically offers reduced hourly rates in exchange for some up-front membership fee buy-in, often with minimum usage requirements. This has no implications of ownership, the members are unlikely to have any say in decisions, it's just a business offering some kind of bundle to high-usage customers.
BTW, note that the difference between wet and dry rates could easily be another $50/hr.
-harry