While categories do have custom fields, think of them as a weblog add-on and not their own entity.
In other words you wouldn’t use categories in the absence of a weblog.
You could think of them as a tag - a way to mark up content such that you can at some point on your site pull out that specific group. So tags, but with a pre-defined vocabulary and the opportunity to structure them hierarchically with subcategories.
Here’s an example from a client site. They’re a catalog retailer for Jeep parts. The weblog contains all the parts information for all models of Jeeps built after 1976 (roughly 4K records).
We broke the catalog down using categories and subcategories. The top-level categories in this case are AC & Heater, Axle, Body, etc. And then within each of those categories there are subcategories for Model (CJ, Wrangler, Cherokee, etc).
So if you wanted body parts for a 1978 CJ5 you’d first choose Body, then CJ, and get to this page.
The image is stored in EE as a category image for the CJ subcategory under the Body category in the Parts Catalog weblog.
Each part listed on that page is one post in the parts catalog weblog. I could - if they wanted to and had the data - make each part number clickable and build a detail page for that specific part.
If their business was structured such that all body parts were handled by one employee I could add custom category fields to hold his name, phone number, etc.
Or if lead times or a return policy was different across parts categories (like most often you can’t return an electrical part once it’s been installed, where other parts are still returnable) that could be put into a custom category field.
Does that help?