Yes it's a mess: there were standards but they were introduced quite late and not universally followed.
In the sizes you mention, using overall diameter (i.e. not the bead, but the outside of the rim), roughly:
26x2, 26x2 1/4, and 26x2 1/2x 2 1/4 (used to be labeled 26x 2 1/4 fits 2 1/2" rim) all go on rims a bit over 22". These rims are mostly Westwood pattern (dropped centre).
26x 21/2 BE rims were used in the day - a bit over 21" - BUT all modern 26x2 1/2 tyres are designed for 22" rims. You have a problem if you have 21" Westwood rims.
650x65 tyres also use 21" rims, but very flat base. No tyres available, but a 26x3 usually works OK.
26x3 goes on a rim about 20.5", almost always with a curved base - not as flat as a 650x65.
28x3 rims are usually about 22.5", and always flat base.
So there, a nightmare these days, but there was sense there once.
Cheers
Leon