When a GFCI breaker pops, is there a way to tell whether it popped for the GFCI reason or because of excessive current?
If the circuit is under normal load - not over the limit, e.g. at 60% of the rate when the ground fault occurs, the sound of the breaker will not be very different from an overload - in case of no shortcut. Especially if inductive devices like big motors or transformers are interrupted.
There is a small chance to distinguish a GF (if the normal load is zero or low, say < 30% of the rate) from a current overload by measuring the wiring/panel connections/breakers with an infrared thermometer.
The breakers do only trip if the overload current (f.e. 2 times the rated current) is flowing for some seconds/minutes, during that time the wiring is heated up above the normal temperature. In case of a shortcut (f.e. 60 times the rated current), the breaker should trip within miliseconds. In that case it might be possible that the wires/connectors could have not enough time to heat up in order to distinguish the shortcut from a ground fault by measuring the temperature.
I can say that for a Square D QO or Homeline GFI breaker, there's no visible difference. The trip indicator shows orange, and the handle moves to the middle regardless of the trip reason. This is the behavior of the GFI breakers that I have used, but it might be worth looking up an instruction manual for your exact brand to see if there is a hint to the trip reason.
Also, you can observe the breaker in its tripped state, then reset it, then use the TEST button to purposely create a GFI trip and see if there is any difference in appearance. This may or may not tell you anything, but its free and easy.
Check on the breaker: RCD usually have an indicator telling if has been triggered the RCD or the MCB part.
ABB has a blue piece of plastic that remains invisible if MCB trigger and pops out if RCD triggered, BTicino has a little window changing color if MCP have opened the circuit.
These checks has to be done with the device still off after the fault (never re-armed).
Others have a blue or white lever that is for the RCD and a black lever for MCB, if both are down RCD tripped, if only the black one is down MCB has tripped.
Breakers vary. Read their instructions/labeling
Every brand of breaker provides a way to distinguish between these. For some manufacturers, the method can be a little byzantine coughSquareDcough. Others have LED lights that plainly indicate; some even have flags. But if you read the instructions and labeling for that model of breaker, it will describe how.
If you don't like yours, check the latest breakers UL-Listed for your panel, and see if they've improved. Or you can look at breakers UL-Classified for your panel such as Eaton CL or CHQ.
Plug the appliance into a different circuit
Specifically one that has a plain breaker and a GFCI receptacle. Then it will be obvious whether the GFCI recep has tripped or the breaker.
Change the breaker to a plain breaker (temporarily)
If you are dealing with a hardwired situation, e.g. modifying wiring, and you just can't tease the trip type out of the breaker, then change the breaker to a plain one. Now, obviously, it won't be a GFCI breaker. Unfortunately this requires you to also move the neutral back to the neutral bar.
Change the breaker to plain (permanently) and fit a GFCI recep
In this case, you fit a plain breaker, and fit a GFCI receptacle at the first outlet location, protecting the rest of the run with the LOAD terminals on that GFCI. You could also fit a GFCI deadfront anywhere along the cable; my favorite place for a deadfront in utility space is right next to the service panel. I mount a 4-11/16" square box there with a 2-gang mud ring, and a conduit nipple into the panel, then fit up to 2 deadfronts in that large box.