Not limited to GE motors... same procedure but different RPMs for the Pratts too.
I sure hope the RPM on the ground is not different.
The orignial posters question did not clarify when the run-up was to be performed (in the air or on the ground)
Ground opereations are quite different and more prone to create engine ice because the idle RPM is much lower than flight idle and/or the engine sucks air and depresses the temperature compared to the outside air temp. The idea behind the runups is to blow the ice loose on the core entrances before it gets big enough to cause blading damage. Hence the timing of the runups.
The N1 RPM is extremely important since it takes windage from the fan to do the job. Since all big fan engines are similar the 60% number should be constant across the fleets. The recommendations (read your manuals) were intended to be similar to avoid confusion and ole wifs tales among the pilots. Thus the wording should be very similar among the various manuals. If they ain't then confusion is going be there.
For some engines, fan blade icing may occur either on the ground or in the air. Again the idea is to shed the ice before it gets big enough to cause pilot distractions or downstream damage. However it's centrifugal speed that does the trick so some (engine specific variations may be found.