NAS = File-level storage, normally accessed via CIFS/SMB/NFS, the NAS device controls how the data is written to disk and the client just sends file-level commands
SAN = Block-level storage, normally accessed via iSCSI/FC, the client device has block-level access to the storage (in theory at least - in reality the SAN may do the actual writes and just present a block-level device to the client)
Whether you need a SAN or NAS very much depends on what you plan to do with it. If you need block-level storage (e.g. for virtual machines) then you need a SAN. If your clients directly access files on a Windows-based system then you probably want a NAS. If you want both then get Unified Storage that does everything (many devices offer this now).
Do you have any way or working out the IOPS on your current storage to make sure any new device will meet your needs?