You SHOULD get different results from a two-point protractor vs. a single-point one. If your cantilever is tangent to the groove at a single point near the middle of a side, how could it also be tangent at two, seperated points? That's not possible without moving either the cartridge or the arm.
With the stylus mounted at any given distance "X" from the arm's pivot point, the arm will need to be farther from the spindle for a single-point alignment than for a two-point alignment.
Since that's what you observed, all is normal in the universe! ;-)
The exact difference in arm mounting distances required by two different protractors will depend on the precise null points used by each, as Jhorowitz128 already alluded to.
One good example of the importance of this is the frustration experienced by many Rega (type) arm owners who attempt to use a Baerwald (two-point) protractor. Rega (type) arms are designed for single point alignment and Rega specifies a mounting dimension 223mm from the spindle. Unless your cartridge has a very long cantilever, achieving Baerwald alignment with this setup will be impossible. You'd have to slide the cartridge farther forward than the slots allow. To achieve Baerwald alignment with a Rega (type) arm and any normal cartridge requires that the arm be mounted closer to the spindle, 219-220mm works quite well. Now the stylus can reach the two Baerwald null points.
It helps to have a turntable with a pivoting armboard, like my Teres and many others. This makes adjusting your tonearm mounting distance a simple, 30 second operation and you can use any protractor you please. If your table has a fixed mounting distance, you're usually stuck with whatever alignment method the designer had in mind.