Are rugby and American football similar?

In many regards, yes. In many regards, no. The main similarities are that ball-carrying players are tackled by the opposing team to keep them from scoring the ball in the end zone. The ball is a similar shape, but a different size. The main differences are in the number of players on the field at any given time; 15 players per side in rugby. 11 players per side in football. Also, in football, a player can advance the ball by throwing it forward to a teammate. In rugby, the ball must travel laterally or backward to a teammate by hand. The ball can only be advanced by running or kicking the ball.