I suspect based on this mine (16280) is a mix master of little value that needs quite a few parts.
Yours was rebuilt at Springfield and, except for the missing parts, is the way it ought to be for an armory rebuild. Clean it up and replace the missing parts, and you will have a great Spencer carbine.
I think my friend's Spencer (33646) is a nice example in need of a new sight spring, front band, and a couple of screws.
Your friends is just the way a soldier would have brought it home from the war. Neat find, and great family history. See if you can find who the soldier was and get his service records from the National Archives.
Here are some observations:
16280 has a 3 groove sleeved barrel
This should be 50 caliber and take 56-50 ammo. Springfield sleeved the barrels down to 50 caliber for the new ammo when they rebuilt these carbines in 1867-74 About 11,000 were rebuilt and updated. Interestingly, they were considered second class arms and were issued mainly to state troops and settlers.
33646 has a 6 groove solid barrel
This is the original 52 caliber barrel and takes 56-56 ammo.
16280 has a square notch in front of the trigger
The notch is for a stabler magazine cutoff, which is missing from your carbine. They are not hard to get. About half of the Springfield rebuilds had cutoffs installed.
33646 has a nicely fitted, rounded profile, in the same place
No magazine cutoff on this one.
16280 has a grooved magazine tube end cap (don't know the name)
This is an M-1865 magazine. Some rebuilds had them installed, others were replaced in service after the war. No problem with it.
33646 has a smooth magazine tube end cap (don't know the name)
This is the original M-1860 mag.
16280 has a spring that moves the extractor
This is the Stabler magazine spring modification. It was installed in the Springfield rebuilds to make single loading easier. Notice that the top of the frame where the breechblock comes through has been rounded off. This is also to make single loading easier.
33646 has no spring to move the extractor
That's the standard M-1860 configuration
Both have 22 inch barrels
Both appear to be model 1860
That is correct
I think they are both 56/56 caliber but the bore of 33646 looks larger than 16280 when held side by side.
16280 is 50 caliber, and 33646 is 52 caliber.
I think the breech of 16280 goes to a different, perhaps later, carbine.
The breech was changed when 16280 was rebuilt. It is correct. Also, when carbines were rebuilt, the frames were buffed and re-color casehardened, which often removed the "Spencer Repeating Rifle Co." markings. The fact that those are missing on 16280 is no big deal.
Judging from the look of the frame where the hammer nose hits, 33646 has been dry fired A LOT! I suspect that you will find that it has pretty good dent in the right side of the chamber. If you try to load it without fixing the dent it will probably jam. Other than that, it's a good looking carbine.
The good news is that both of those carbines are correct and with a little work would clean up nicely and could be made complete. Congratulations!