AFAIK (Feel free to correct me on this)
Cat D is light cosmetic damage, (Something like it was keyed or needed a bumper painted)
Cat C can be repaired but more than 50% of the cars value, (So needs new panels and possibly straightening)
Cat B is parts only
Cat A is crushed.

TBH, It wouldn't bother me, Many many cars get repaired without going through insurance and people are none the wiser.

Saying that it will always have a stigma associated with it, So if you plan to sell in a year or 2 might be a bit awkward.