King First Move
A King’s first move is special because it determines the castling situation. The first move of the King must be castling, otherwise you lose the “castling right” for the rest of the game. Any King move loses the right to castle, even if the King moves back to its original square. Generally speaking, it is far better to “castle early” rather than leave your king in the center, where it will come under a dangerous attack.
Once the issue of castling rights has been resolved, there is nothing special about further King moves. The King can move slowly, 1-square in any of 8 directions, forwards, backwards, sideways, diagonally, and can go back and forth as desired. The King can even castle on one side of the board, and then later run to the other side of the board (e.g. to escape from an attack), or up to the other end of the board (e.g. to support a passed pawn in an endgame).
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