Not really. The application doesn't care. Hell, many of these modern serverless frameworks are built so that they can run both server and serverless from the very same codebase, so it is likely you can take the same code built to run on someone's MacBook running macOS/ARM and run it on an EC2 instance running Linux/amd64 and then take it to a serverless provider on any arbitrary hardware without any code modification at all! I've been around the web since Perl was the de facto way to build web apps, and it has always been an exceptional situation to not have the hardware fully abstracted away. Typically, if it will run on one system, it will run on any system.

The move away from CGI/FastCGI/SCGI to the application being the server was a meaningful shift in how web applications were developed. Now that we've started adopting the server back out of the application in favour of the process-based model again, albeit now largely through propriety protocols instead of a standard like CGI, serverless has come into use in recognition of that. We don't want to go back to calling it CGI because CGI is no longer the protocol du jour.