Difference between Groups and Sets?

Groups: You can combine several dimension members into a single member using groups. you can't use in groups in calculated fields.

example1: if you are working with a field that contains thousands of products, you can use Groups to combine those products into higher level categories. Grouping data is also really useful for cleaning up data inconsitencies. 

example2: your data may have California listed as CA, California, and Calif. When you try to see all sales in California your numbers will be split across these three rows. You can quickly group these three variants together to treat them as a single value.

Sets: Sets are custom fields that define a subset of data based on some conditions. A set can be based on a computed condition, for example, a set may contain customers with sales over a certain threshold. Computed sets update as your data changes. Alternatively, a set can be based on specific data point in your view. You can use sets to compare and ask questions about a subset of data. 

For example, in a scatter plot showing product sales, you may select the products with the most sales and add them to a set. You may then create another set that contains the products with the highest return rates. With these two sets you can ask questions like "What percent of my total sales is from high returned products?" Or you may go further and compare the two sets to each other to create a new set that contains only high sales products that are also returned frequently.