I think heading is the direction the boat is pointing and course is the actual path the boat is taking. This takes into account set/run effects of the current/wind.
Different vendors might have different definitions..
This is from the manual of my Furuno NN3D MFD8
Description of orientation modes
Head-up: Displays the chart with the current compass heading of your vessel at the top of the screen. The heading data from a compass is required. When the heading changes, the boat icon remains fixed, and the chart picture rotates according to heading.
North-up: North is at the top of the screen. When your heading changes, the boat icon moves according to heading. This mode is for long-range navigation.
Course-up: The chart picture is stabilized, and shown with your current course (overground) at the top of the screen. The boat icon moves with the heading. If you select a new course, the picture resets to display the new course at the top of the screen.
I might be wrong - but the "If you select a new course" statement above indicate that they are talking about "selecting course as selecting new way point"
I switch between North up and heading up depending on what I'm doing.
For inshore navigation I prefer HU, for orienting and planning I switch to NU.
I know the difference between COG and heading.
My plotter also have a heading line and a COG/SOG predictor (that is independent of the orientation mode.