Big differences, with shared php hosting you get: (Yes, I'm sure there are exceptions, but they're... exceptions)
Payment per month not per usage. Normally there are usage tiers and a "you reached your limit" page rather than scaling.
No versioning beyond standard file operations.
No routing. You get all traffic in a single endpoint.
Only web traffic, no integration. Serverless in many cases is FaaS, with multiple event sources, not web-request-handler-aaS.
Sure, there are some similarities. But the use cases are completely different. Nobody is seriously considering "should I use AWS lambda, or GoDaddy shared PHP hosting?"
> Serverless computing, also known as function as a service (FaaS), is a cloud computing code execution model in which the cloud provider fully manages starting and stopping of a function's container platform as a service (PaaS) as necessary to serve requests, and requests are billed by an abstract measure of the resources required to satisfy the request, rather than per virtual machine, per hour.[1]
> Despite the name, it does not actually involve running code without servers.[1] The name "serverless computing" is used because the business or person that owns the system does not have to purchase, rent or provision servers or virtual machines for the back-end code to run on.
For example, nearlyfreespeech.net neatly fits even the pay-for-what-you-use billing definition here