While I realize the most obvious difference being that serverless is also a deploy framework that "abstracts" the cloud, I think one of its primary benefits of adoption is that it also does a good job (in my experience, but I have not yet impelemented things deeply with it) emulates services very well where needed, for instance, DynamoDB[1]
If it was without that, I think it would be a lot less useful and way less easier to adopt, so I think its just as important to the story.
Why on earth AWS doesn't have their own first party emulators for everything I still don't understand to this day. I credit that for why Firebase & GCP are easier to use, because they have a good local development story for alot of their services (Firebase in particular has an emulator suite for nearly all their services)