I am currently using it for what you could probably call a user interface. My use case is forms stored in S3 served as an iframe which POST via JS to AWS API Gateway that calls lambda to process the form and return the result to the user.
Correct. That being said, there's nothing stopping you from emitting, say, HTML from such a function. But there's nothing really helping you either.
It's basically function calls in the cloud; a remote procedure call where the remote procedure is executing on their infrastructure.
I'm also guessing there's no session state or cookies?
We'll I guess there wouldn't be without a server. You'd have to use JWT or the like.
Or any server side store, maybe DynamoDB.
the functions are stateless, but you can access S3 and DynamoDB.