It differs in that you don't have to worry about scaling up that HTTP server, or pay for the machine hosting that HTTP server. With Lambda, you only pay per requests, current rate is $0.20 per 1 million requests.
Is there also any limit on machine resources that a single request can use? I'm curious about cases in which requests might need non-trivial amount of computational power.
You pay for request time too, measured in 100ms increments. And you pay more for more CPU/RAM.