The main difference is that the Windows Store only allows software that was written specifically for the Universal Windows Platform. So what does that mean? Well, in part it means that UWP applications run in a sandbox and are generally more limited that Windows desktop apps. This isn't all bad; UWP apps are much safer because they run in a sandbox, and they are better at protecting your privacy. A "normal" desktop exe file can access pretty much anything on your Windows PC, and if it is a malicious file that means trouble.
There are plans to bring more powerful desktop apps to the Windows Store, but Microsoft is still working on making that happen and I'm not sure when they will be available.