Pop` wrote:

....

If it's happening when something start/stops or has a healthy inductive
load, it's pretty much normal. The phases of currents in the wiring goes
out of phase momentarily, allowing enough current difference to trip the
GFCI.
....
Don't think so. If the instaneous currents in the hot and neutral
are not exactly opposite, you have a lot of electrons going
(or coming from somewhere). Unless you think that they are
getting saved up in the drill (for a rainy day?), then they
are going somewhere (probably to ground) and you have a ground fault.

If the Test and Reset buttons work fine, you're probably in good
shape.
FYI, the Test switch places an imbalance across the GFCI's Load side to
check its trip capability; same as a defective appliance would do. The
drill is inductive, and the grill heater probably is, too.
Heaters are rarely inductive. They are almost purely resistive.

Another possibility is, it did its job in the scenario you described.

Try the drill on another, different GFCI in the house and see if the same
thing happens. IF it's the same brand, it's pretty likely repeatable. If
so, don't worry about it.
If the drill causes two different GFCIs to trip, you had better
worry about it.

You could try an extension cord too, from another GFCI and see if the
trips repeat. If so, no worry.

Different brands of GFCI will work slightly differently but usually they are
repeatable for things like this.

Just for grins, you might check the polarity of the hot/neutral too, in the
outside outlet/s to be certain the polarity is correct. And be certain the
earth ground is present in the receptacles so 3-wire devices are properly
grounded.
Good to check, but neither of those should cause a GFCI to falsely trip.

A lot of people don't use them outdoors for just that reason unless it's a
pool lighting system, things like that; the motors are kept off them and are
earth-grounded separately as they're designed to be.

What reason? That because of moisture, outdoor loads are more likely to
have ground faults and trip the GFCI?