NAS is just Network Attached Storage, they are both the same type of device. Its just the LinkStation has some extra features like a BitTorrent client built-in so you can set it up to download movies and tv shows automatically - if that BitTorrent thing doesn't make sense to you then its not a feature you need probably. Either will do fine for what you need, but if I may I'd suggest looking at the D-Link DNS-323 or 321 as I've found it to be a much better network attached storage device.
First off, I should say that I have lots of these devices plugged into my network not only for my music/movies but also because I'm a photographer so need lots of space. The advantage of the D-Link type device is that it is way faster than any Network drive I have used or have including my Buffalo and Lacie network drives and that can really make a difference when you're copying lots of data across the network. Secondly, the D-Link is an empty box with room for up to 2 hard drives so you can put whatever size drive you want in there. I'd suggest buying it with one 1TB drive to begin with. The other great feature is that if you buy 2 of the same size drives and put them both in there it has RAID abilities, and in case that doesn't mean anything to you just think of it as automatic backup. It constantly keeps the exact same data on both drives so that if one fails, you can just replace it with a new one and you haven't lost any data which can be important if you're spending a lot of time digitizing your music and movies. It is a little more expensive than the ones you're looking at initially, but I really wish I'd just bought it first before buying the single network drives with hard dives already installed such as the ones you're looking at. Don't worry if you're not a computer person, you simply slide the hard drive into the box, it is very easy to do. Link to UK amazon site below if interested.
If you have your heart set on the Buffalo drives, either will do to be honest. It can be easier if you look for a device that has UPnP media server support as iTunes for instance will automatically find all the music on the network drive for you. The D-Link does have it and the Buffalo LinkStation specifically says it too has it, although the DriveStation does not mention it. I know I've thrown a lot of info out there, especially if you're not that into computers and you just wanted somebody to say get this drive model.
If that's what you're looking for, I'd buy the D-Link and add one of the 1TB hard drives Amazon has links to on the same page. If that doesn't appeal to you, I'd go for the LinkStation since it too specifically mentions iTunes media server and may be easier for someone not into tech to have the drive find the songs for them.
http://www.amazon.co.uk/D-Link-Bay-Network-Storage-Enclosure/dp/B000GK8LVE/ref=sr_1_1?ie=UTF8&s=electronics&qid=1242356365&sr=1-1