This is a bit of a broad question, so this is a broad-stroked answer.
In general, a NAS is more of an appliance than a server. The OS is not as full featured as a dedicated server OS, but it has an interface to let you share files. A common feature is to have different RAID levels (0 & 1 almost always, 10 and 5 common) available for data availability. This increases uptime, since a single drive failure (other than RAID 0) will allow you to continue to work. It is not backup, since if you lose the NAS in a fire, you've lost everything. There are plenty of other features, but I'm sure that there are other better descriptions of NAS elsewhere.
The good news is that less features generally means less care and feeding over time. But there's also less functionality as well. You won't necessarily be able to install any arbitrary application on it, like SQL Server.
In your case, since you're talking about a file-server replacing NT (!), a simple NAS may be worth considering. The big questions that only you can answer are how much downtime are you willing to accept, and how much are you willing to spend to mitigate that risk.