Gain margin and phase margin in Nyquist plots
It is the same margin of change.  If the Nyquist plot for open-loop gain just touches -1, then there is one or more poles exactly on the stability boundary (i.e., the real part of the pole in the s-domain is zero, or the z-domain pole's absolute value is 1).  At that point the system is metastable, and nudging the pole ever so slightly beyond that point will render it unstable.

If you're starting with a stable system, and you don't let your poles cross the stability boundary, you'll end with a stable system -- that's the idea behind phase and gain margins.