THE SLOWEST PIECE COVERS TWO SQUARES IN ONE MOVE
The king moves to one adjoining square, which is the shortest move in the game. In a corner there are three such squares, on an edge five, in the middle of the board eight: nearly a threefold difference, and that is why the king is walked towards the centre in the endgame and hidden in a corner at the start.
There is one exception, and it is also the only move in chess in which two pieces move at once. Castling is described as a king move rather than a rook move: the king is transferred two squares towards the rook, and the rook is then transferred to the square the king has just crossed. That is why in a score sheet castling occupies the king's move and not two moves.
The conditions for castling are not about the squares but about the history of the game: neither the king nor that particular rook may have moved before. The right is lost for good after the king's first move — even if it comes straight back to where it started.