In catalogs, you obviously set up and manage catalogs. on top of that, you are dealing with categories too. It is worth mentioning that you are seeing catalog structure one store at a time, which you can switch in the store picker dropdown.
How does catalog builder work?
Through catalog builder you can either navigate to find a category you are looking for or you can create catalogs and categories.
More about categories
Category levels are configured per catalog and can be as wide and deep as you wish. In each category, you have the ability to create subcategories and place products.
The same product can be configured in multiple categories, catalogs, and stores without copying the product. You simply add another reference between the product and the category in question.
Catalogs further control available price lists or price groups. You can also set allowed price groups for the catalog - to enable switching between multiple price groups for the individual customers.
Examples of this would be easily enabling multi-currency scenarios, e.g. a price group per currency you wish to support. Or differentiated pricing scenarios by enabling multiple price groups with the same currency, but with the price overridden on a per-product basis.