There is actually no difference at all. A common conversation when discussing receptacles may be referring to a ground fault circuit interrupter (GFCI) as simply a ground fault interrupter (GFI). They are generally the exact same thing.

What happens if you hook up a GFCI backwards?

The GFCI is miswired due to reversal of the LINE and LOAD leads. The GFCI cannot pass its internal test, indicating that it may not be able to provide protection in the event of a ground fault.

Does a GFCI have to be grounded to work?

A GFCI does not need a ground wire in order to trip properly. A GFCI simply trips when a fault is detected on the neutral wire. An ungrounded outlet will not trip using your tester.