The key difference here is that Zappa and the other frameworks emulate the API (or SNS, SQS) service on your local machine. This means that if you want to test an API that requires authentication or if your Lambda function is triggered by some other async event, you cannot test it locally. You'll need to deploy it first.
SST on the other hand, deploys your app and when a deployed Lambda function gets invoked remotely, it'll stream that request to your local machine, execute it, and send the results back to AWS. So you get the advantage of working against real infrastructure while still making changes locally.
SST on the other hand, deploys your app and when a deployed Lambda function gets invoked remotely, it'll stream that request to your local machine, execute it, and send the results back to AWS. So you get the advantage of working against real infrastructure while still making changes locally.
The video helps a illustrate it a little better — https://www.youtube.com/watch?v=hnTSTm5n11g