Orientation and permutation: EO, CO, EP, CP

Every piece has a position (permutation) and a twist or flip in that position (orientation). Methods differ in which of the four they solve together: CFOP does orientation (OLL: EO and CO) then permutation (PLL: EP and CP); COLL does CO and CP together; ZBLL does everything once EO is done.

An edge is 'good' if it can be solved with R, L, U and D turns only. Quarter turns of F or B flip the four edges they move; nothing else changes EO. ZZ fixes all twelve in its first step, which is why its F2L needs no F or B turns and its last layer always has a cross.

A corner is oriented when its top or bottom colour faces up or down. Corners twist in thirds: the total twist is always a multiple of a whole turn, so a single twisted corner never happens on a real cube.

Once oriented, pieces only need moving. Permutations come in cycles: a 3-cycle moves three pieces round, a swap exchanges two. On a 3x3 an edge swap always comes with a corner swap (they share a parity), which is why no PLL swaps a single pair of edges alone; 4x4 'PLL parity' is exactly that case.