"I believe with a 120V circuit, if the amount of current on the hot
wire
does not equal the current on the neutral wire, the breaker will trip.
The theory being the current is going somewhere unwanted, like through
your heart...

However, with a 240V circuit, with 2 hots and a neutral, how does this
work? It would seem my breaker is tripping if there is any current
difference between the two hots, in which case using 120V is not
allowed. "

I believe with a 240V GFCI, at any point in time, what goes out on one
240V leg must equal what comes back on the other plus neutral. If any
current goes somewhere else, eg through you to ground, it trips.