In the "no-code" system, the end user does not write code. In the "serverless" system, the end user does connect to a server.
It doesn't just "have" servers; they aren't a hidden implementation detail. Connecting to a website is an instrumental part of using the software.
In the "code" system the end user does not write code either - that's the developer's job. In the "no code" system it's the developer who doesn't write code, and in the "serverless" system it's the developer who doesn't set up servers.
"Serverless" refers to the demarcation point in the shared responsibility model. It means there aren't any servers about as much as "cloud hosting" means the data centers are flying.