Would this be a regular circuit breaker fuse? Otherwise what's different?

If single phase you'll notice sometimes it has a little extra ground wire connected (now mostly obsolete), for 3 phase it doesn't, in both cases it will say so on the outside (typically: the test current, and usually there is a test button which makes them easy to identify, this test button forces a small leak causing the circuit to become unbalanced resulting in a trip (if it doesn't trip when the test button is pressed the breaker is considered faulty and should be replaced).

For instance, here is an 'Eaton' 3 phase breaker with integrated ground fault protection circuitry:

https://www.omnical.co/products/eaton/1742431/2259595

Note the little yellow 'test' button. That's a 30 mA fault current device, you can have higher permissible fault currents for certain gear that tends to be a bit more leaky which would otherwise cause nuisance trips. These little things are quite the work of art inside, if you ever have a faulty one I would encourage you to pick it apart to see what makes it tick.

Circuit breakers trip when there's too much current going through the circuit (enough to melt the wiring for example), and so protect from short-circuits: hot and neutral touching each other, or a short in equipment.

GFCIs protect against current leaking to ground, by detecting if the current flowing on a hot and neutral leg are different. If they're different, the current must be going somewhere else: to ground, through you, etc. The GFCI breakers do this in the breaker, the outlets do it at the outlet. As someone else mentioned, you can also have other non-GFCI outlets chained to a GFCI outlet, so that upstream outlet is the one that pops if there's a fault.

TL;DR they detect and protect against different fault conditions.