GFCI is US/Canada-specific terminology. The more general term is residual-current circuit breaker (RCCD) 
- Note that a GFCI does NOT protect against overcurrent or overload. Thus, a device that uses a GFCI must have a circuit breaker upstream of it to prevent overload or fire hazard.
Protecting Downstream Outlets
A useful feature of a GFCI outlet is that if you connect outlets downstream through the GFCI - the downstream outlets will also be protected with the GFCI functionality. See:
I just got shocked from a functioning GFCI, so this is a real data point. I tested the GFCI with the test button. It works. Then I touched a part (3D Printer heat bed) that had a frayed wire (not intentionally). I think what happened was that I got no shock when touching with one hand, but then I touched it with my second hand on another part of the 3D Printer bed - which I am led to believe closed the circuit to a return wire. The GFCI did not trip. I don't fully understand what exactly happened, but this answer is consistent with me closing the circuit, so there was no leakage to ground. I think if the device were grounded, a breaker would have tripped, so it looks like grounding a GFCI-protected device is a good idea.
- UK version -