So, for singles, no accents, it would all be taps? Correct me if I'm wrong.
In this particular context, yes. And for all accents, it would be all full (free) strokes.
If on a page of notation you see singles with no accents, the author will either designate a stick height, or use dynamic symbol (piano, mezzo forte, fortissimo, etc.), or both.
Caddywampus -- If a student were only to practice the different strokes one hand at a time, he will find it very difficult to play combinations of the strokes with both hands, because the INTERDEPENDENCE of the two hands has been neglected. Furthermore, the 3rd "stroke" you mention: where is it's height? Is it up to the student to decide?
Try this: play groups of 4 notes -- accent, accent, non-accent, non-accent, and so on. Left to only 3 strokes, you will not be able to accomplish this pattern as quickly, or as dynamically, as you would with 4 distinct strokes.
The 4 types of strokes are a learning tool, to get the student thinking about not just how to hit the drum, but to control where the stick goes before and after each hit. They are not meant to be an absolute, all-or-nothing guide to technique. There are many refinements to be achieved in between these strokes, and you will encounter them as you attempt to play various rudiments and pieces, at various tempos and dynamic levels. The 4 stroke approach leads to maximum dynamic range and maximum control, and therefore, to maximum expression.