Well, there are specific hardware configurations that are designed to be servers. They probably don't have graphics cards but do have multiple CPUs, and are often configured to run many active processes at the same time.

But for the most part, "server" is more related to the OS configuration. No GUI, strip out all the software you don't need, like browsers, and leave just the software you need to do the job that the server is going to do.

As to updates, this also becomes much simpler since you don't have a lot of the crap that has vulnerabilities. I helped manage comuter department with about 30 servers, many of which were running Windows (gag!). One of the jobs was to go through the huge list of Microsoft patches every few months. The vast majority of which, "require a user to browse to a certain website" in order to activate. Since we simply didn't have anyone using browsers on them, we could ignore those patches until we did a big "catch up" patch once a year or so.

Our Unix servers, HP-UX or AIX, simply didn't have the same kind of patches coming out. Some of them ran for years without a reboot.