Charles III was for years described as a 'King in waiting', nobody was confused that perhaps he was already king just because the phrase used that word.
I don't think in English usage there is any meaning attached to 'acting X' which 'caretaker X' (as you're happy to call it) doesn't also carry. Both are used interchangeably, the former you'd put on your CV, the latter might be used by the media when your employer put out the less release announcing it, but same thing: for some reason there is not currently an X, but you are fulfilling some necessary duties that that person would do in the meantime.
When used in a narrow sense "acting X" can capture it, but then sometimes people start to use it somewhat interchangeably with "interim X" etc. and it depends on the specifics what happens in successions etc.
I don't think in English usage there is any meaning attached to 'acting X' which 'caretaker X' (as you're happy to call it) doesn't also carry. Both are used interchangeably, the former you'd put on your CV, the latter might be used by the media when your employer put out the less release announcing it, but same thing: for some reason there is not currently an X, but you are fulfilling some necessary duties that that person would do in the meantime.