I missed the centerpull rear brake. I also see that the seatstays do not have the nice fluted caps of the V so I will guess that they are plain steel (and the chainstays) instead of Cr-Mo like the V. But I will bet the main diamond is Cr-Mo on the bike Anniversary.
At $45 I'd grab it. Fuji made good bikes. Those 12 speed wheels you are looking at are probably spaced 126, not 120 which the Anniversary might be. I'd still do both. You can cut 6 mm off the axle, remove a few spacers and have a 120 and the Anniversary might be a 126 anyway. (This was a time of change in the industry, 120-126 standard. Fuji was a little slow in general and liked the SunTour narrow spacing, so it is not given which way this bike is setup. But it is also old-fashioned steel. It can be cold-set to whatever spacing you want.
That's a frame you can do a lot with. It will all be standard Japanese English tube diameters, headset, BB, etc. Common metric for threads. Parts from almost anywhere will drop on it. There's a chance I am wrong about the 27" wheels but if you find that is the case, well getting back the $40 for those alloy wheels would not be too hard and they would be very welcome at any bike donation center. If it is the 27" standers, that's cool because it allows you to go 700c with some longer brakes (Mafacs will fit easily), then run big fat tires and fenders for a super winter bike. SS or fix gear will be easy with the horizontal dropouts. (I have done the 27" to 700c switch on at least 4 different bikes over the years, most of which I then set up fixed.)
Ben