Terminology note:
Waypoint: A marker at a set of coordinates, with a name and a little icon, maybe a proximity alarm.
Trackpoint: The dots that make up a Track (usually[1] a recorded path travelled).
Routepoint: A Waypoint or map feature that makes up a Route (a planned path that you intend to follow).
POI: A marker from a separate file you don't normally interact with that's rendered on the map to show you where, eg. petrol stations are.
I assume Courses (a proprietary Garmin thing that isn't part of the GPX standard) have Coursepoints, which are analogous to Routepoints?
[1] FCVO 'usually'. These days people routinely generate Tracks in order to follow them, as devices can handle a lot more points in a Track than in a Route.
To expand on the above.
Coursepoints - software (planners) that can handle Courses and Coursepoints if asked to export as GPX (which does not accept those constructs) will, IME, convert Course to Track and Coursepoint to Waypoint.
Waypoint: A oair of coordinates wrapped in code that says "this is a standalone Waypoint". By convention Waypoints are information-rich, having a Name, often a marker Symbol, and various information fields such as, for example, road names (for a crossroads) or a phone number (for a hotel). All this information may or may not be accessible on your GPS.
Routepoint: (Commonly also called a Viapoint) a uniquely-named pair of coordinates wrapped in code that says "this point is part of a
Route". Begs the question of "what is a Route?" which does not actually have a straightforwardd answer at this stage, but NB my use of Uppercase to distinguish "Route" from "route" - which latter as every fule kno is simply a way of getting from A to B. (NB that this is not, generally speaking, what cyclists do - they mostly ride from A to A.) By convention the Routepoints that make up a Route are spaced apart by 500m or more, on average - but this is just a convention and not a rule. There's a lot more to be said about Routes but we are not interested in Route files here.
Trackpoint: A pair of coordinates wrapped in code that says "this point is part of a
Track". Begs the question of "what is a Track" and traditionally it is a 'breadcrumb trail' of recorded progress through space and time - known as a "
Tracklog" - but this primary purpose has been somewhat hi-jacked over recent years, so that a Track could also now be drawn in software then used as a 'Route-Lite' (which is what cyclists most commonly do) - pretty much like a highlighter line drawn on a paper map.
Trackpoints can be very minimalist - for example they are not individually named (unlike Routepoints) - although if they are part of a Tracklog they will include Elevation and Timestamp information at least (again unlike Routepoints), and often with modern GPSs a heap of other metrics such as heart rate and power etc. By convention the Trackpoints that make up a Track (or Tracklog) are closely spaced, less than 100m on average and often much less - but this is just a convention and not a rule. Because of the extra metrics recorded, and the (over-)close point spacing, modern Tracklogs in GPX form can be very large files (they are smaller as FIT which is generally a superior - but less universal - format).
A GPX file can contain any number, and any combination, of Waypoints, Routes and Tracks. However not all software - and certainly not all GPSs - can handle all the variants of 'combined' files. In addition there are various limits on point counts, most of which are now historical in nature and not practical limits for users of modern GPSs. The limits are therfore more of interest to Organisers who seek to provide files of maximum compatibility across a range of devices. Even so, the old 500 limit (which is for Trackpoints per Track) is only going to be relevant to a vanishingly-small number of riders, who probably know who they are and how to deal with it. The most important thing for Organisers IMO, is to know that they should be providing a Track file (and not a Route or combined file - tho Track+Waypoints can be good). Unfortunately many Orgs farm the provision off to RWGPS ("download your GPX from this URL") and then it is all too easy for the unwary user to export the wrong type of file, or at least a sub-optimal one.
I would say that any GPS model introduced in or after 2009 (when the Etrex 20/30 was introduced) has enough practical capacity that limits need not be a consideration. Unfortunately modern Planners have also become a bit bloated, and liable to export over-large files. It is worth bearing in mind that some GPSs (Etrex 20/30 series) do have a Trackpoint limit of 10,000 (per Track) and I have seen plenty of files generated by RWGPS (to name but one) that easily exceed this over a longer distance. Your options then are to split the Track, or simplify it (Phil's site is good). NB that in the case of a GPS, error messages are scant and the first you know about it not being happy may well be halfway round a 400 ...