They may not be!
The old way of measuring tyres was the overall diameter x width. The more modern way is to measure the rim diameter x the tyre width. The old system also assumed the tyre had the same height as it's cross section.
The later system is less likely to provide a mismatch of tyre and rim. For example, all 19" tyres will fit on 19" rims but there is a recommended rim width for each width of tyre - the widths used to be classed WM1,WM2,WM3, etc. - nowadays, it is more usual to find the widths quoted in inches (1.85, 2.15, etc) even though the world has now gone metric!
So the original size tyre (25" x 3") would actually fit on a rim 19" diameter (measured to the bottom of the rim - not the overall diameter of the rim), as would a 24" x 2½" tyre. It would appear that the third option of a 24" x 2¼" tyre would require a rim of slightly larger diameter (19½").
Regards,
Eddie.