I think the nomenclature comes from the fact that "traditionally", before you can upload a piece of code somewhere and have it executed, you have to first setup

I think the nomenclature comes from the fact that "traditionally", before you can upload a piece of code somewhere and have it executed, you have to first setup a server, as in: an instance of a particular operating system (a physical server or a VPS), hence the name "server-ful". In the "server-less" paradigm, you upload directly to an abstract cloud and have cloud infrastructure execute your code. Moreover, uploading to "a server" implies using a fixed, pre-allocated set of CPU/memory/disk resources that cannot grow dynamically, while "server-less" implies using dynamic infrastructure that can scale CPU/memory/disk resources up and down as needed and/or clone executed code across multiple internal compute instances controlled by a load balancer and so on - the notion of "a server" becomes no longer relevant.