Technically speaking there is no difference. NAS is a Network Attached Storage. By definition it is just shared space on a network that is shared out at the file level and not the block level. A Windows server is technically a NAS.
Now, in implementation there are some difference. Typically NAS devices run on lower performance hardware than a full Windows server, often times pre-built and even proprietary hardware. As stated above, most are built on Linux and have a user interface for management, diagnostics, etc. NAS devices can be pretty easy and simple for small businesses to set up as they don't have to go through installing Windows, installing drivers, etc. However, they also do have limitations compared to standard servers running Windows. For example, your NAS devices are made to be only that, network shared storage. You won't be able to set it up to do anything else, such as running a website or install additional software on there. It runs only the specialized OS and only shares files (though some new NAS also have built-in features for cloud connection, ftp, etc.)
A Windows server will allow you to install additional roles or software as needed to do additional things beyond just what's included within the operating system. You can also upgrade or replace parts easily within a standardized Windows server, where as this may not be the case in a NAS device.
So the last thing I'll touch on here for now is scaling. NAS devices, just like servers, come in a wide range of performance capabilities to meet different scales of needs, from simple home devices to large businesses. Given the size of the network you are talking about, you are looking probably at some of the more expensive and powerful NAS devices which, generally, are very close to the same hardware as your servers albeit still probably towards the lower performance side compared to a similar Windows server. A full enterprise NAS device is going to offer many of the same features as a similar Windows server physically, such as redundant power supply options, RAID, and multiple NIC interfaces. However, it may not be as flexible (such as additional hardware support) and may even cost more than doing a similar Windows based server.
So, my recommendation for storage solutions may not be what you are looking for, and it definitely may not be what everyone else would recommend either. But for small environments with limited performance needs for storage may be advantageous to look into a NAS instead of a Windows storage server. However, for larger businesses, such as what you are talking about, it may actually be more cost effective to look into a standard server running Windows Server as you will get the same features plus some more, but at the same cost if not perhaps even cheaper than the enterprise NAS solution.