Generally, the point guard takes the ball up the court, sets up the offense, and facilitates the ball to give their team a chance to score. Point guards are often referred to as floor generals, which means that they get the rest of their teammates in the right positions on offense. Additionally, they will be the ones who get most of the assists off made baskets. Point guards can also be their team's main scorers, though, as players like Stephen Curry and Damian Lillard do in today's NBA.
Shooting guards are slightly different from point guards in that they don't facilitate the offense to get their teammates as the point guard does. The main duties of a shooting guard are catching-and-shooting and cutting to the basket. They also like to drive to the basket. As a bottom line, shooting guards need to be able to score the basketball. Some prime examples of shooting guards in today's NBA include Klay Thompson, James Harden, and CJ McCollum.
A "combo guard" refers to a player who is capable of playing either point guard or shooting guard. Combo guards are becoming more and more common in the modern game. You can learn more about combo guards by checking out the Basketball Combo Guard tutorial.
Overall, the biggest difference between point guards and shooting guards are that they fill different roles on the court. There are some broader differences-such as height and statistical trends-that come into play as a result of this, but the facilitating vs scoring roles are the largest differences.