The simple answer is both. Let me explain. First what are categories and tags? On a wordpress blog, a category is a way to group your posts into like subjects, and tags highlight key things discussed in that blog post.
For example you could write a post on vegetable gardening and assign it a category of “gardening”. But inside that post you discuss growing tomatoes and peas, so you would assign the tags vegetables, tomatoes and peas to the post.
You can look at categories like a table of contents and tags as an index. The categories group posts into like subjects, and the tags indicate where individual things are discussed in all your posts.
To take our gardening example a bit further, you could also have a post on making homemade spaghetti sauce. The category would be recipes and the tag could be tomatoes, among others. Make sense?
In wordpress, every post must be assigned a category. But using tags is optional. Tags offer an additional way for your readers to find the information they are looking for. In our examples above, if we had not used tags at all, a user would have a harder time finding our content that discusses tomatoes.
A good rule of thumb is a post should have only 1 or 2 categories assigned. But you are allowed to use as many tags you want. That said you don’t want to get too carried away and tag everything. Tags lose their usefulness in that case.
If you use tags, do so sparingly and be strategic in the tags you use. The tags should be relevant to the content and the subject. The post should also contain a fair amount of content relevant to that tag to warrant tagging it. In our recipe example, tomatoes are very relevant to a spaghetti sauce recipe, but a tag such as salt really is not all that relevant. Think if terms someone would search on to find the content you have written. That will help determine good tags to use.
I hope this helps you understand what categories and tags are and how to use them. Now you get to decide if you are a tagger or not!