Are discount stores and outlet stores the same thing?

To the buyer, yes.

In theory the outlet store does not have a distributer between the factory and the store, and thus should be able to sell cheaper.

A retail store is one that sells to the public, so an outlet store is a retail store. The difference is that an outlet store is owned by the company whose goods it sells, it sells mostly, or exclusively, that company's goods, a lot of the time it sells the "seconds"--good stuff that wasn't quite good enough to bring full price--and it's usually in an outlet mall. They used to claim the whole place was full of seconds, but there's no way anymore; outlet malls have become a major industry, and any company whose quality control is bad enough to keep a couple hundred stores full of rejects would go broke quickly.