A lot depends on other things.
As the first responder said. If the ATS is working, then a delay period after the generator starts the switch transfers from SHORE to GEN, and everything keeps working, no harm, no foul, no damage.. Same when you shout down switching back to SHORE.
But if you have some big ticket items running then.. Well
Water heater is a big current item.. That much current may cause FLASHOVER on the ATS contactors.. This can weld them so it kills the ATS. Does not harm the generator.
Microwaves likewise are big current draws, and may also blow an internal fuse.
Air Conditioenrs (motor driven stuff) not only big current draws, but there is an INDUCTIVE Kick, so they will spike the voltage as well when the ATS breaks (The ATS is a "Break before make" meaning it disconnects from shore power BEFORE it connects to generator.. NEVER are the two connected together) This is far more likely to cause Flash over and damage the ATS.
If you don't have an ATS.. Then you have a generator powered outlet somewhere you plug into to use the genny. So nothing bad happens.
HINT. always shud down A/C for 3 full minutes when transferring.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times