Changing vs. Shortening - is there a difference? Yes!
A quick primer: Changing the course means moving the existing marks. You still use all the same marks, they are just moved to a different place. Shortening course is when the competitors can't finish in time and you finish at an existing mark. No marks are moved, but you finish at a new finish line "short" of the existing finish line.
If the race committee changes the course, they display a "C" flag with some indication of how to find the changed location of the next mark, and they make several repetitive sounds to get your attention. The race committee tells you that the course changed and how to find the next mark. The rule is written like this:
33 (a) If the direction of the leg will be changed, the signal shall be the display of flag C with repetitive sounds and one or both of (1) the new compass bearing, (2) a green triangle for a change to starboard or a red rectangle for a change to port.
Shortening Course can happen when the weather turns bad, the wind turns bad, or for any other reason affecting safety or fairness. By its nature, shortening course happens with little or no warning. To shorten course, the race committee will display an "S" flag at the next available turning mark, sound two horns, and finish boats as they cross a line between the "S" flag and the mark. The rule is written like this:
32.2 If the race committee signals a shortened course (displays flag S with two sounds), the finishing line shall be, (a) at a rounding mark, between the mark and a staff displaying flag S; (b) a line the course requires boats to cross; or (c) at a gate, between the gate marks.
32.2 The shortened course shall be signalled before the first boat crosses the finishing line.
The primary difference is that a change of course is done at the mark starting the leg that is changed. A change of the location of the next mark means the whole leg is changed. A shortened course happens immediately as soon as the "S" flag is displayed. There is no warning. The recommendation from US Sailing is that the signal to shorten course should be made as soon as the boat is on station and the competitors are close enough to hear and see the new line.
Always fun! Hope this helps.