Yeah it's a little confusing to describe the difference. But what most of the tools currently do is, locally mock a Lambda function execution. You cannot test anything beyond that.

For example, if your Lambda function publishes to a SNS topic that invokes another Lambda function. You can only test this locally my mocking the inputs for the first one, testing that. And repeating it for the second one.

With SST, it deploys this stack to AWS. So when you trigger this workflow, both the Lambda functions get invoked on your local machine. You don't need to mock anything. It is as if they were invoked live.