In general there is not much difference between categories and tags in WordPress. WordPress categories have a hierarchical structure. This structure can consist of multiple levels. There exists a relationship between the terms. For example, there is a parent-child relationship between books and fiction:
When editing your post you will see:
Tags are not hierarchical, which means there’s no relationship between the terms.
To understand the difference between the two think of a book. Categories would be similar to the table of contents and tags would be similar to the index at the back of the book. Reading a book with an index at the back, really comes in handy.
Categories exist to help you identify what your blog is really about.
Tags are meant to describe specific details of your posts.
In general you can use both or either. However you shouldn’t tag a post for the sake of tagging a post, you should tag because it is helpful for the user.
On the site I created Cashmere Crafts you can view an example of how to use categories and tags in a way that is useful to the user.