@NikNik, I've been on the other side of the fence too. I had some major neurosurgery years ago, and my Hubby had to be my carer while I recovered. I had always been the organiser, and suddenly my short term memory was so shot that I'd forget something from a minute earlier. I had reduced mobilty and co-ordination, significant fatigue, and all sorts of other neurological functions glitching.

It was very hard for me to accept help, made harder when official organisations weren't very accomodating. I didn't look "disabled", and sometimes because of that others expected more of me than I was able to handle. I remember days when I went home from a difficult situation in a really bad state of exhaustion that would take a day or two to recover from.

But as hard as it is to accept the need for care, "carer" is probably the most honest descriptor. @Mazarita mantioned the importance of sensitivity, and maybe part of that is allowing people to use terminology that they're more comfortable with, but for official purposes, "carer" probably gets the necessary response. Some of the more informal and comfortable terms might get dismissed as less relevant.