Let's not confuse a pass versus a lateral.
A ball thrown backwards(in relation to the line of scrimage) is a lateral, whether it is thrown overhand or underhand, and is a live ball whether it is touched or not.
A ball thrown forward(in relation to the line of scrimage) is a forward pass, whether it is thrown overhand or underhand and is an incomplete pass if it is not caught by a player before it hits the ground. If the ball is thrown forward by someone that is past the line of scrimage it is the same as forward pass and ruled incomplete with a penalty added on. Some times this is referred to as a forward lateral.