Once upon a time WordPress only provided the user with a category option. Categories essentially worked as an organised sorting system which associated similar posts with each other making it easy for users to sort their posts and readers to find similar entries. This worked well until bloggers began to have extensive category lists when they were trying to sort their blog posts. It made it hard for them to describe a post in more specific terms so they created the wonderful tag we use so easily today!
Tags are different to categories as they don’t necessarily have to have any relationship to the post. In social media they are used to direct traffic. This is true for blogs as well however they are more commonly used to help provide meaningful connections to your posts, and for readers to click on and find other posts with the same tag.
WordPress actually do a great explanation of the two, click here to see what they had to say about the two.