From what I understand, "Cloud" basically means that you still have to deal with servers, whether they be VMs or physical devices, but all of the networking and loadbalancing aspects are abstracted away. "Serverless" takes it a step further and makes it so you don't even have to deal with setting up VMs, you just give the provider the code you'd normally run on a host, and they'll automatically handle all of the infrastructure stuff, like spinning up extra hosts under heavy load.