(eg. Would a USA starter work in the UK, or UK starter work in the USA)

Might be a stupid question but I've always wondered if this would work?

4-22W starter for two lamps in series (Choke) operation (Like Philips S2 and the Osram ST151), will work in the USA, but with only single lamp. Others I don't know.

There are two loosely established starter categories : 110-120V and 220-240V. You must use the one that is appropriate to the circuit, regardless of which country you're in.

Philips S2, Osram ST151, N. American FS-2 are all in the 110-120V group. They can be used for single lamp choke circuits on 120V or series circuits on 240V.

Philips S10, Osram ST111, N. American FS-4 are all in the 220-240V group. They can only be used for single lamp circuits, a choke on 240V or an autotransformer ballast on 120V. Autotransformer ballasts have an extra winding to raise the open circuit voltage in the 220V range.

If you use the wrong starter, it will not work. A 220-240V starter on a 120V circuit will simply not heat enough to close the contacts so the lamp won't light. A 110-120V starter on a 240V circuit will not shut off when the lamp has struck and will perpetually try to strike an already lit lamp, giving a good impression of an EOL lamp. If left long enough, either a lamp electrode will break effectively turing off the circuit, or the starter will get stuck.

There are other starters than the ones I listed, and they are more fine-tuned for specialty lamps such as circline, 4-8W lamps, etc. but the general principle is the same.

Just a note: The starters are linked to the voltage of the lamps (and that is then linked to the certain minimum OCV mentioned above). So lamp sufficing with 120V OCV requirements needs the "120V" starter, even when operated at e.g. 230V (those lamps may operate two in series on a common ballast on 230V). It will somehow work with the "230V" starter as well, but it will last shorter (the higher voltage starter will let the lamp glow with cold electrodes, sputtering them).