At E3 this year, Xbox chief Phil Spencer confirmed that Microsoft is indeed working on a new generation of Xbox consoles, in case there was any doubt in your mind. Since then, we've learned that the new consoles are codenamed Scarlett, and that they'll arrive in 2020.
According to a report from Thurrott.com today though, there will be two separate next-gen consoles. One will be similar to gaming consoles that we see today in terms of functionality, but the other will be dedicated to streaming games.
Called Scarlett Cloud at this time, the service will stream games with a limited portion of it running locally, helping to cut down on latency. As Thurrott puts it, the games are running in two places at once, and uses "Microsoft's cloud to stitch it all together". The report says that there would also be less latency if the game runs off of Azure, since it would be physically closer to the multiplayer server.
It would seem that Microsoft is working on its game streaming service right in the open with FastStart. The new feature allows you to start playing games while they're still downloading, which is the first step toward being able to play pieces of a game as they're available on your machine.
You'll still be able to play the same games on both consoles, as the company isn't trying to create a disconnect there. Indeed, it's done a lot of work with backward compatibility to try and push the idea that you should be able to play all of your games on the same console.
The streaming-only console should be significantly cheaper than the full console, and they'll both be arriving in 2020. According to the report though, the streaming-only variant is further along in development.