When you hear that a NAS is a “file server”, what that means is that the protocols used (typically AFP, SMB or NFS) provide access to the data at a file level. Your computer says “give me file foo.txt” and the NAS “file server’ hands back the file. The software running on the NAS takes care of file locking, etc. The NAS also has the actual on disk file system (ext*, HFS, ZFS, NTFS, etc).
A SAN on the other hand simply gives a block device to your computer (you often hear of SAN storage called “block storage”). Think of it like a really long SATA or SCSI cable going from your computer to the SAN array. Your computer then puts a file system on the disk. When you access a file on a SAN volume, things work essentially like they do for a local disk. Your computer reads a stream of bits from a specific location on the disk and handles all of the file locking, etc (clustered SAN file systems add some extra parts in here, but that’s another topic).
Files, database files, applications, etc are all just files to the storage system and computer. Files are fundamentally just streams of bits. As far as the storage system is concerned there is no difference between them as it doesn’t really understand the content of the file.
As a general rule you can put any files on any kind of storage (local disks, NAS storage or SAN storage). There are a few times you run into something that is really picky and “smart” about where it is and will only work from a very specific location, but that’s the exception to the rule. The real question is should you put a specific kind of data on a specific kind of storage. That all depends on the specifics of your situation. Without knowing more about your specific environment and uses, it’s hard to say if it’s a good idea or if it will work as you would like.
Hope that helps.
Chris