Server or NAS?
As illustrated above, servers come in many shapes and forms. Your PC (or Mac or Linux machine) can be a server and, in fact, does just that when it is sharing files or a printer. So can a rackmount dual, quad or bazillion-core computer that is specifically dubbed a server. But servers can come in "appliance" form, too, with focused features and simplified interfaces. NASes fall into the latter group.
You might be getting the feeling that the definition of "servers" is pretty broad. Experience has shown that when there is something that is fuzzily defined, the marketeers will jump in to "help". Not too long ago, they tried to convince us that home "routers" and "gateways" and "firewalls" were different things. But they all performed the essential task of taking a single Internet connection and sharing it among multiple computers. And even though it drives networking pros crazy, most consumer networking product manufacturers have given up and called these products "routers".
NASes seem to have had it easy up until now, with manufacturers pretty much sticking to the "NAS" moniker. But Microsoft has decided it wants into this exploding market. So they spent a lot of money at CES this year and have partnered with HP to try to convince consumers that want they want is a Windows® Home Server. Here we go again...
The point of all this is that it doesn't matter whether something is called a Home Server, NAS, Home Storage Server or even "Bob" (well, maybe that last one would matter). In the end, if it doesn't do what you need it to do, and you've spent your hard-earned money on it, then it will be called something that we're not supposed to print. So focus on the features of prospective products, not what they're named.
Before I get into the choices that you will need to make, let's cover those that you won't, by looking at the features common to all NASes:
File Sharing - All NASes provide the basic function of networked storage—just like your computer does when you enable file sharing. But NASes have their own little computers in them and so use much less power, take up much less space and generate much less heat.
TIP: A good rule of thumb is that a NAS uses about 15 - 20 W of power per drive. So a four-drive NAS will typically draw 60 - 80W in operation.
Ethernet Connection - All NASes also connect to a LAN via 10/100 Ethernet, with newer models also supporting gigabit Ethernet. But not all NASes with gigabit LANs support jumbo frames, probably because manufacturers don't want to be hassled by the support calls that can be generated by mixing jumbo and non-jumbo frame clients.
NOTE: "Jumbo" frames are Ethernet frames larger than 1518 bytes. They can help speed up file transfers, if the processors in the NAS and your computer are fast enough. In order to use jumbo frames, every device involved in the transfer—your computer's Ethernet interface, LAN switch and NAS Ethernet port—must all support them.
SMB / CIFS support - The lingua franca of networked filesystems is SMB / CIFS, which is supported by most modern OSes thanks to the work of the open source Samba project. This means that a NAS should work with Windows, Mac OS X, Linux, etc. Other networked file systems are sometimes also sometimes supported, which I'll get to later.
Web browser - based administration - As with most consumer networking products, NASes are administrated through browser-based interfaces. The main gotcha is that products tend to come with Windows-only utilities that help you initially find the NAS and change its IP address to match your LAN.
So if you're not running Windows, you may need to probe around a bit to find your NAS' initial IP address. Fortunately, most NASes come set to automatically acquire their IP address settings via DHCP, which reduces the range of possible addresses that you'll need to check. In most cases, you can log into your LAN's router and find the NAS' IP address in the DHCP client list.
Expansion via USB 2.0 - With few exceptions, all NASes have one or more USB 2.0 ports. Among other functions, these ports can be used to connect a USB hard drive, which can be used to back up the NAS internal drive or be shared on the network.