C2, there're 2 types of approaches straight in and circle to land.
Aircraft categories are defined for a straight in, as you've stated, as per Vat.
Circling, missed approach and take off aircraft categorization is defined with max speed for maneuvering. The relevance of this is that for a straight in approach you'll use the minima for the declared category by the operator regardless of the Vapp flown whereas for circling you'll apply the minima for the actual speed flown. Best example for that, again as you stated, is when you're CAT C for a straight as per PANS OPS but gotta fly a circle to land as per TERPS. Automatically you'll be in the cat D for circling thus using CAT D minima.
