I actually doubt that Chinese chess is based off the Chess that came from India. Influenced maybe, but not 'spread' to China from India.
They do share in common the following: A "tower" piece that moves in straight lines, a head piece that must be taken to win and can only move one step at a time and a "cavalry piece"
They differ vastly in: the existence of a river, pieces move on lines rather than squares, its a General rather than a King, there is no Queen, there are cannon units that move like Rooks but "eat" by jumping over another piece. "Elephant" pieces move in squares of fours and cannot cross the river. The General piece and two Aid pieces cannot leave this box area, the Cavalry piece move in a zig-zag shape rather than a L-shape. Infantry pieces are like pawns and move one step at a time but once they cross the river, they can move in any direction and the General pieces should never face each other or one of them will get eaten.