I’ll start off with what they have in common. Both are excellent tools for search engine optimzation and findability within queries if used correctly. Within wordpress when creating a blog post you can find a place where you can choose your category and tags for each individual post. By denoting both category and tags you can give your posts a boost in search results by making your content easier to find and define.
Visualize your blog as a book. Now think of your categories as the main chapters and your tags are like subsections within that chapter. Say you are online shopping for clothing; you may see mens, womens, child, infant, and so on across the top menu. Those would be your categories. Within these categories would lie your tags, for example, pants, socks, underwear, dresses, etc. Those would be your tags.
When implementing and choosing categories don’t have too many or it gets too confusing for the end user. Also utilize your main keywords into the category names at that too will rank you higher. Categories also organize your online content so that if someone reads a post in a certain category and wants to read more of a similar nature, then all they need to is click on that category name to find all your posts relative to that category. There is also the option within wordpress to “show related posts” which will place 4 or 5 thumbs at the bottom of your post of related posts as per category.
Tags also help to organize your content but are much more specific in nature. By searching or clicking on your tags, users can find all your content relative to that specific term or keyword only. By finding your content quickly, your bounce rate drops and your page retention rates go up, as the end user can find and peruse the information they are seeking quite readily.
Whichever or whatever way you decide to go, be sure to use these two valuable tools to your advantage.