App Engine is PaaS: You provide your app to the service in a runnable form (maybe a container image, maybe not) and they spin up a dedicated server (or slice of a server) to run it continuously.

Lambda is Serverless: You provide them a bit of code and a condition under which that code should run. They charge you only when that thing happens and the code runs. How they make that happen (deploy it to a bajillion servers? Only deploy it when it’s called?) are implementation details that are abstracted from the user/developer as long as Lambda makes sure that the code runs whenever the condition happens.

So with PaaS you have to pay even if you have 0 users, and when you scale up you have to do so by spinning up more “servers” (which may result in servers not being fully utilized). With Serverless you pay for the exact amount of compute you need, and 0 if your app is idle.