The short version:
People are assigned to opportunities, never to categories. They are connected to a category only through the opportunities inside it, and that single rule explains most of the confusion between the two.
It is the unit of work, and it carries the three things that make a program run:
Approval also happens here. Somebody is approved for an opportunity, and that is what lets them see and reserve its shifts.
It groups opportunities, and it has its own Category Dashboard with three tabs:
From the same dashboard you can copy the category's public link, edit the category, and add a new opportunity straight into it.
Categories also shape what the public sees, because they organize how your opportunities are presented on your organization page.
No. There is no such thing as being assigned to a category.
If you want somebody involved in everything under a category, you assign them to the opportunities within it. This trips people up when they expect one assignment to cover a whole program.
Ask whether you would ever want to report on the group as a whole, or show it as one thing to the public. If yes, it is a category.
A food bank might have a Warehouse category holding sorting, packing and loading opportunities. Each is scheduled and staffed separately, but the board only wants one number for the warehouse.
The common mistake is the reverse: creating a category per event, which leaves you with dozens of categories holding one opportunity each and no useful grouping at all.
Every opportunity belongs to one, so in practice yes. The real question is how coarse or fine to make them, and coarser is usually better than one per event.