Elephant calvary appears to have been one of the original chessmen; however, precisely how the first elephant moved is less clear. The elephant has also been subject to more variation in regional games than any other piece.
The most probable move is what's now called an alfil (Arabic for "the elephant"): jumping diagonally to the second square. This is the move in shatranj and is the weakest version of the elephant. Triply colorbound, the alfil can only reach an eighth of the squares on the board.
Another leaping possibility is the dabbaba: jumping to the second square orthogonally. Slightly more powerful, this move is still doubly colorbound and can only reach a quarter of the board. This move was not widely adopted.
The most powerful of the early elephant moves is the one the Japanese called a silver general: stepping any diagonal direction or orthogonally forward. The five directions it can move are said to represent the elephant's four legs and trunk. This move became the standard across Southeast Asia.
All three of these early moves had some currency in Indian chess. Later varieties of Indian chess also lead to a fourth possibility: the rook move. This was because at some point, the chariot was replaced with a camel, but because a camel is weaker than an elephant, the incongruity was resolved by swapping thier moves. As such, depending on time and place, any of these moves might have been applied to the camel instead.
When shatranj reached Europe, the elephant was subject to additional changes. The (largly abstract) Islamic piece form was reinterpreted as a bishop and eventually gained the move now called by that name.
Before gaining unlimited range, various (more limited) experiments were tried. ...