Server-less is the new paradigm where the server is in the cloud. More specifically, you're not maintaining any server, you just supply callbacks written in the language of your choice, and the infrastructure figures out how to package them in containers, deploy, run, scale and dispose when no longer needed.
Can you explain what you mean with "server is in the cloud", is it like literal placing a fog machine to make some kind of cloud around your servers or placing a server inside another server, such as a raspberry pi within a PC box?
It is, but taken literally and not helpful in infrastructure discussions.
"Serverless service" as recently coined means you're not concerned with the server layer. Either the hardware one, or the "http request server" one. What you provide is functions that execute on some action. As long as the API is preserved it doesn't matter if it's one server of one/multiple providers, cloud deployment, room filled with monkeys at keyboards, linux running unicorn, windows running iis, or anything else.
It's one level above "set up your services and upload code for specific server" PAAS. And two or so levels above "set up your own servers and services" IAAS.
PS. I don't think sdees matches the definition of serverless as it's commonly understood.
> Ah I see, so serverless service is a way to say "I am so high up higher than your puny little cloud down there".
I don't believe there's any judgement in "serverless service". Depending on your requirements you may want this solution or you may prefer something else. It got a name, because when you get tired of saying "model more abstract than PAAS but based on the same principles of being independent of the infrastructure" you invent a short name - servers got abstracted, so it's "serverless".
> its just funny how our industry invents new words every year or so, it gets hard to keep uptodate.
The industry doesn't invent words. It invents new solutions. If they get popular they get names, so it's easier to communicate. That's how every industry works.