[OJFord]

What distinction are you making between 'acting X' and 'caretaker X'?

I'm British, not American, so I'm not assuming something like the vice president automatically becomes president, we don't have that either. If anything it's even less than Germany since (at least in theory and history, modern media etc. makes it a bit different in practice) there's nothing special about the PM, it's just the governing party's leader. I suppose though you could say the heir apparent to the throne immediately becoming the monarch on the death of the previous one is like vice taking over - but I don't think that detracts from my point because nobody would call that 'acting monarch', they just are.

'Acting X' means doing the necessary duties, but not any major decisions that can be avoided/deferred, while the 'real' replacement is found. Sometimes it ends up being the same person, e.g. the head of some division is 'acting CEO' for a while as the board searches for a new CEO, ultimately ends up going with that person and title changes to just 'CEO' - or they don't, and go back to old job, or maybe quit in a huff, and the person they found is just 'CEO' taking over from the 'acting'.

[RandomLensman]

The real issue here is that people stick to the word "Chancellor", not the "acting" as such.

There is no named role of "Acting Chancellor" created in the basic law, instead someone is just tasked with performing certain duties (and people might sometimes call it "acting Chancellor" or whatever). However, the position "Chancellor" is a well defined & special role (unlike perhaps PM) and whatever that other "acting" role is, it isn't a Chancellor. It is a bit like adding Oliver Cromwell to list of English Kings or Kamala Harris to the list of US Presidents - you can do it but you then move beyond the "standard" definitions.

[OJFord]

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.

[RandomLensman]

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.