There are different measures of 'disability' - there's the (incredibly strict blue badge test, the PIP test and what is considered a disability at work... and many more no doubt).
Criteria include how long something might last for (2 years +), how much it affects you etc. Some disabilities are always changing, and people really struggle to understand why sometimes I might have crutches and other times now. They ask annoying questions like "oh, are you cured/no longer disabled now", when it's that I'm having a good day. On bad days people tend not to see me as I might not be able to leave the house.
Psychologically it's hard to identify as disabled, even when outsiders might all be in agreement that you are. So basically it is not clear cut at all.
My Occupational Health doctor at work list me as disabled under the Disability Discrimination Act, but even then comments that that's only his view and these things are never decided until decided in a court of law (i.e. if I had to take employer to court for breaking the DDA), and even then, the disability status would only exist within the meaning of the DDA, it wouldn't affect blue badge status etc.
I've preferred to not identify as disabled generally, but now realise I need to sometimes, for example using my OH report to get a disability card from my train company, meaning I can have a bit more authority when I ask to use priority seats.