Posts are the primary content type of most WordPress Sites, and are usually quite numerous. As a result, WordPress includes a few features to help publishers organize posts, making them easier for readers to find.
Categories are a hierarchical method of organizing the site’s posts. For instance, if you have a site that offers reviews on automobiles, your categories would likely include “Cars,” “Trucks,” “Motorcycles,” and “Scooters.” You can have subcategories as well; hence, under “Cars,” you might have “Sedans,” “Luxury,” “Sports,” and “Hybrids.” An author can assign a post to any number of categories.
Tags are a way of attaching keywords to blog posts. Unlike categories, tags aren’t organized into any sort of hierarchy. Essentially, they allow you to be more granular in your classification of content.
Using the previous example, a post could be filed under the category of “Cars,” and then be tagged with “Maroon,” “Maruthi,” and “i10.”
As a general rule of thumb: categories organize content, while tags label content.
Any WordPress theme should enable content publishers to use either method of organization, and should make allowances for both in the theme design.