Categories vs Tags (WordPress)
The main difference between categories and tags is one of scope: categories are broad containers that hold posts with similar content, whereas tags are labels that are attached to posts to indicate minor points of similarity.
A Recipe Website
A cookbook is organized by the types of dishes it contains: breads, meats, poultry, vegetables, desserts, etc. As a website, these chapter would be categories, with each recipe comprising a single post. Clicking on the category "Breads" would bring up all recipes in the bread category.
Each post could then be tagged with a each ingredient (flour, eggs, cinnamon, etc.) and cooking technique (baking, frying, grilling, etc.). Clicking on the tag "eggs" would bring up all recipes that contain eggs, while clicking on the tag "frying" would bring up all recipes that use frying, regardless of which category they are in.
This example emphasizes the type of dish. By using ingredients for categories, it could also emphasize the main ingredient.
A Movie Website
For a movie website categorized by genres, each genre (Horror, Drama, Comedy, French New Wave, etc.) would be a category. Tags could then be used to indicate actors, directors, etc.
The purpose of categories and tags is to make your website easy to navigate. Therefore, you can save a lot of time (and headaches) by planning how you want your website to be organized before you start creating a lot of posts.