Shatranj has its origins in Chaturanga and is the predecessor to modern European Chess. The two games resemble each other, but Shatranj is different enough that they can be considered two distinct games, even though it is Shatranj that Europeans first called "chess".
The main differences between shatranj and modern chess are that the earlier game had a vizier instead of a queen, and an elephant instead of a bishop, and these pieces had much more limited movement than their modern counterparts. The pawn also lacked the double-step introductory move it has today, and furthermore, there was no castling.
While all this sounds very limiting, it can make a refreshing change from modern chess. Modern openings must be left behind, and the pace of the game is a little slower, the limited movement of the pieces allowing defenses to be set up before the opponent approaches to destroy them.
Shatranj Kamil was an early and largely unsuccessful attempt to expand the game of Shatranj.