The key difference between hydride and methyl shift is that a hydride shift can occur when a hydrogen atom moves to a carbon atom bearing a positive charge from an adjacent carbon in the same molecule, whereas methyl shift occurs when a methyl group moves to a carbon atom bearing a positive charge from an adjacent carbon atom in the same molecule.
The terms hydride shift and methyl shift come under the subtopic of carbocation rearrangements. Here, either a hydrogen atom or a methyl group moves to a charged carbon atom from an adjacent carbon atom in the same compound.
