Craft Commerce Categories and Product Types
Product Types are really for the content of the fields and field layout of each product plus basic options for things like tax/shipping category defaults.

For full categorization in menus and site structure, we recommend putting a category field on all products.

For example you might have a category field names 'department' which you put all products into.

You then could show all products related to that category: https://craftcms.com/support/entries-related-to-category

Let me know if you need more guidance in the comments.