What is the difference between the double-slit equations and diffraction grating equations?
The d in diffraction gratings is the slit width.
We use m=0, 1, 2, 3 instead of m=1, 2, 3, 4.
They're completely different.
There is no difference, except that the distance d is the average distance between the slits.
The equation for maxima of double-slits is the equation for minima of diffraction gratings.