FAS is a controller for NetApp disks only, and V-Series is a controller for both 3rd Party Vendor Disks and NetApp Disks (support matrix for 3rd party vendors and switches). There are both FAS and V series equivalents for mid-range and high-end models (FAS3270/V3270 FAS6240/V6240 for example).
vFilers are ONTAP 7-mode virtual containers that create separate virtual filer instances withing a physical controller (doesn't matter if FAS or V-Series).
Just to confuse matters you can end up with vfilers when you add a multistore license to your system which allows you to partition up your controller. In Clustered ONTAP (COT) you can achieve roughly the same thing using vservers.
For more on multistore