The AddCheckpoint family logs a simple checkpoint message which will appear in the standard main view of the Console (like LogMessage). It is mainly used for marking or highlighting important sections in your log (and can be very useful for navigating).
Watches, on the other hand, represent variables (name/value pairs) and appear in the Watches toolbox. They show the latest/current value of a variable (Latest tab) or the value of a variable at a specific point in time (Selected). Watches have a specific type (string, integer, float etc.) and can be logged with the WatchString, WatchInt etc. functions. Integer and float Watches can also be used with the Watches Graph toolbox (Ctrl+F9) to visualize their values over time and display graphs:
There are also Counters which are basically integer-based Watches with simple functions to increment/decrement (IncCounter/DecCounter/ResetCounter).
I hope this helps!