Bishop Moves: Bishops more diagonally, in any of the 4 possible diagonal directions, including two backwards diagonals. It can move any number of squares, but cannot jump over pieces.
Rook Moves: The rooks more horizontally or vertically, as many squares as they can reach. It can move backwards or forwards (or sideways), but cannot jump over pieces. The Rook also has a special role in the castling move.
Queen Moves: The Queen can move horizontally/vertically like a Rook, or diagonally like a Bishop. It can move any number of squares, and can move backwards or forwards. Like a Rook or Bishop, it cannot jump over any pieces.
Knight Moves: The Knight is the only piece that can jump over pieces. Its only move is a jump move in an L-shape, which goes in a 2-1 or 1-2 pattern. The Knight can jump in 8 possible directions, including 4 backwards directions. The Knight captures pieces by jumping onto them.
King Moves: The King is a slow-moving piece, which normally can move only 1 square in any of 8 directions. It can move up/down (vertically), left/right (horizontally), or any of the 4 diagonals, but can only ever go one square at a time. The King also has a special move called the Castling Move, which involves its own Rook almost swapping places with the King.
Pawn Moves: The Pawns move slowly, but have lots of tricks. Pawns cannot ever move backwards. They are allowed to move 1-square forwards normally, but cannot capture forwards. The pawns capture diagonally, but only 1-square, and only forwards (no backwards captures). But pawns cannot move diagonally to an empty square (they can only capture), and they also cannot capture in their forwards moves (they can only move into an empty square). So pawns capture differently from a non-capturing move, the only piece where it is different.
Pawns also have special moves. They have a 2-square forwards move that is only allowed on their first ever move (the first move for each pawn). And they have a move called pawn promotion where they can become a Queen at the other end of the board (or another piece, called underpromotion). And finally, the pawns have a special capture move called en passant which is the weirdest rule in chess.
Advanced Chess Moves
Hence, there are several advanced moves to learn:
There are a number of other general move rules which all chess moves must comply with. For example, you cannot legally leave your King in check. And you cannot self-capture your own pieces. And there are some other restrictions.