The Framestore and gateway are both very different although they are represented in the interface in a similar way.
The Framestore refers to the database bins/clip libraries of Smoke. Its were managed media is stored that is imported into Smoke. So all your clips and timelines are stored in the Framstore Clip libraries and it deals with all the media management tasks including archiving.
The gateway is service running underneath Smoke which allows the Smoke application to browse your local disks/drives/network/SAN. So when you browse through the gateway, you are looking through the Smoke "FINDER" to get to your media.
The idea is that you pull clips from the gateway into the Framestore Clip libraire. The tricky bit here is by default Smoke can link to the material seen by the gateway or you can tell Smoke to Store a local copy. In other words smoke will transcode the file to the framstore database as DPXs. This is useful if you are pulling files over a network and there is a performance issue. By storing a local copy you get around the bandwidth problems of a network. But it's not necessary all the time.
The media import workflow does appear to be moving to a model where all the media will be pulled in (or drag and dropped) from the gateway into the frame store clip libraries.