The confusion between Serverless Stack and Serverless Framework is common. As a matter of fact, I had the same confusion myself. I’ll give you my take and let @frank or @jayair chime with any corrections.
Serverless Stack and Serverless Framework are different frameworks for building serverless apps. Granted, they are similar in that they both allow you to build serverless applications. However, they take different approaches to building serverless applications.
Aside from that, I’d say the primary difference between the two frameworks is the developer experience. The killer feature with SST is the live lambda development environment. I’m also partial to using SST/CDK to create my application infrastructure in code, as it seems more straightforward than the yaml files offered by the Serverless Framework. Using SST, I can iterate and deliver faster than any other serverless offering.
Adding to the confusion is that the makers of SST happen to have the single best resource for learning to build serverless full-stack applications in their Serverless Stack Guide…using the Serverless Framework. You could be forgiven for thinking this implied a relationship between the frameworks, but no such relationship exists. I wouldn’t be surprised to see them eventually offer a version of the Serverless Stack Guide using SST exclusively.
The key takeaway is that Serverless Framework and Serverless Stack are two independent options to build serverless applications. They just happen to share similar names
Oh, and yes, you can use SST within a Serverless Framework application to enrich the developer experience. True to form, they’ve written a fantastic guide on how to do this.