What's the difference between Supergalactic and Equatorial coordinates?
Equatorial coordinates have their equator and poles at the equator of the earth and the poles at the earth each projected onto the sky.
Supergalactic coordinates on the other hand have their equator in the same plane as the "Supergalactic plane", which comes from the distribution of nearby galaxy clusters. And the poles just perpendicular to the the plane.You can kind of see this preferred plane in the image below.
One is therefore just a rotated or tilted version of the other. To be precise the north poles of Supergalactic coordinates lies at approximately RA = 18.9h, Dec = +15.7° in Equatorial coordinates.
See also here here for a comparison of common celestial coordinate systems.