A football team's staff is a lot bigger than just what you hear or see. The coaching positions you will hear the most are the head coach, offensive coordinator, and defensive coordinator. But there are also coaches for every group of positions. Quarterbacks, running backs, wide receivers, tight ends, offensive linemen, defensive linemen, linebackers, and defensive backs all have their own coaches. There is also a special teams coach, who is responsible for making sure the kicking and punting part of the team is set.
Some of the coaches hold other coaching positions as well. For example, the quarterbacks coach for the New York Jets is also the offensive coordinator.
The head coach is the one that calls the shots. They decide who plays in the games and when. The head coach gets the most credit, if not all of it, for the team's success, and gets most of the heat when the team loses. Most of the time, head coaches are former players with years of coaching experience and typically have an expertise in either offense or defense.
Simply put, this is the coach that organizes the offense. It does NOT necessarily mean they call the plays. For example, Sean McVay is the head coach of the Los Angeles Rams but, because of his brilliance on the offensive side of football, is also the main play-caller for the team's offense. In the case of the Rams, the offensive coordinator makes sure that the offense is in line, outside of the play calling.
The defensive coordinator is the coach that is responsible for the defense. Once again, it does NOT mean they are the main play caller for the team's defense. In the event that they are the main play caller, they organize with the coach where the defensive players are supposed to line up and what they are supposed to do during a play.