The wide receiver in football is often the designated position that catches the football. There are usually at least two on the field during each offensive play and they run a pass pattern trying to get open. Receivers get the most catches out of all the positions.
Along with the wide receiver, the tight end is a designated pass-catchers on the football team, meaning that is their main objective. Tight ends line up right next to the offensive line and while sometimes used as blockers mainly go out and catch passes.
The running back can also catch passes but usually as a 'last resort' checkdown option. They sometimes leak out of the backfield to catch a screen or short pass to help their quarterback just get rid of the ball.
In recent years running backs have adapted to become better pass catchers. Guys like Alvin Kamara and Tarik Cohen have been given more of a responsibility in the passing game. They run routes just like receivers and created mismatches with defenders due to their elusiveness and speed.
Quarterbacks catch the ball either in a trick play or off a tip. If the quarterback throws it and the defensive line bats it back, the quarterback can catch it and run with it. They are then credited with a pass completion and a reception. Trick plays sometimes have the running back take the snap or have a lateral, but either way the ball can end up back in the quarterback's hands after a pass.
Defenders are never the intended receivers on a play however they sometimes end up catching the ball. In the event the quarterback throws a not so accurate ball, the defender is allowed to catch it, in what is known as an interception.