Here my 2p's worth Rich, but not sure if it applies to ALL 20" rims & tires,
20X1-1/8 & 20X1-3/8 = 451mm diameter
20X1.50 & 20X1.75 = 406mm diameter (also 1.95, 2.20 etc. tires)
So only 451mm (fractional) tires will fit on 451mm rims and only 406mm (decimal) tires will fit on 406mm rims.
Be careful about what the frame is actually supposed to take as well as the brake positioning will also vary. For new school with lugs, some brakes like LDC have loads of adjustment so can be used on a mini / junior frame with 406mm rims. For old school if you want to put a 451mm rim onto a pro frame you might need to find a smaller roadie style brake.
Hope that helps a bit