Strictly speaking a 'course' is the same as a 'heading', meaning the direction you are currently going in.
A 'route' is a number of waypoints linked together to create series of headings. These normally connect significant trail features such as mountain tops, river crossings or the pub at the end, although they can of course be programmed for any grid refernce. Typically more information can be assigned to waypoints, such a name etc.
There is another term, 'track', which a series of 'trackpoints'. These are purely grid reference markes which when linked together create a more detailed path or route to follow. Trackpoints tend not to have names assigned or any other attributes, hence most GPS units can store many more trackpoints than waypoints. A GPS can be set to log trackpoints at regular intervals to provide a record of where you have been. Typically these 'tracklogs' can be downloaded into mapping software for displaying on a computer.