Ferris Bueller: Good question.

Librarian a category of a certain type of job. From that there are sub categories.

All librarians are old ladies with funny glasses that say, "shhhhh" a lot." is a stereotype.
The term "stereotype" is itself a category.

Things that are heavy = a particular category of things.
All fat people eat potato chips is a stereotype.

A category is a division of classes of things (small, large etc) It's a classification - a group of a particular kind.

A stereotype is the characteristics assigned or generally associated with a particular group. Here there is a bit of a crossover as certain "categories" of groups (liberals) could be given stereotypical characteristics.

But, to say someone is a liberal isn't the same as saying someone IS liberal. The first identifies the category, the second describes the person (and perhaps stereotypes them in doing so).

All liberals have a philosophical leaning that differs in ways from conservative philosophy. Otherwise they'd both be liberals or conservative. A liberal can be a fiscal conservative but a social liberal. (same is true of a conservative - conservative on finances, liberal on views towards social issues).

A stereotype would be to say all liberals are fiscally irresponsible. All religious nuts are conservative. etc