That's not really how GFCIs work. In normal operation, all of the current that comes out of the line pin on the plug returns through the neutral pin. When a ground fault occurs, some of that current doesn't make it back to the neutral, and this causes an imbalance. A GFCI senses that imbalance, and if it is greater than just a few milliamps, it removes power.
The actual implementation is pretty clever. The line and neutral wires (black and white in North American practice) but not the ground wire are run through a magnetic core shaped like a donut. A sense winding is also wound around the core. If the currents in the line and neutral wires are exactly equal and opposite as they should be, their magnetic fields cancel in the core and no current is induced in the sense winding.
One reason for nuisance trips of GFCIs are radiofrequency interference filters built into devices with switching power supplies (which is just about everything these days). They include capacitors that shunt the radiofrequency noise onto the ground wire. If these capacitors are too large, they'll pass enough current to reach the trip threshold of a GFCI.
Another cause are devices that simply generate too much radiofrequency noise that isn't properly filtered. GFCI sense circuits are pretty sensitive, and if they don't filter out radiofrequency noise from a load it can also cause nuisance tripping. This is probably what's happening with your large pool pump; variable frequency motor drives can generate a lot of noise if they're not properly filtered.