I have two Macs in two rooms. Both have just macOS (High Sierra).
I would like to log into either one from my user account, and find my files the way I last edited them on either Mac.
Accessing one's account from any one of multiple linux machines is a common arrangement on that OS. All CS departments do this with hundreds of linux PCs.
Is the same possible with Macs, perhaps through a RAID attached to a dedicated Airport Extreme?
The term "Server" in macOS Server seems to point to the ability to host a web server. I don't understand why that is an additional feature when one can run a server on vanilla macOS just fine. Does the term "server" here refer to the ability to access one (or multiple) account(s) from any one of multiple Macs in the same LAN?
Context + comparison with Linux/Windows solutions
On Linux machines (in CS labs) the speed to access one's files is formidable. It's all but impossible to tell that the files are not local but on an NFS. MS Windows has something similar, but the speed is pathetic. So much so that all users always end up storing a lot of files on their local machines (even in 2017) just for the file read/write operations to be good; it's extremely slow to access files on Windows servers.
Ironically, a Samba server running on Linux and serving Windows machines is a far superior solution. Have you tried a Mac-only solution (with either of the two scenarios you suggest: dedicated NFS or one Mac dedicated to be a server)? Is the file read/write speed in roughly the same league as files local to a Mac?
Update
The question is becoming too broad. I'm forking the two sequel questions: