The range of all possible reps is like a continuum.
Kinda like... (assuming these are near your rep-maxes)
1-3 Neural Adaptation
4-6 Strength
8-12 Growth
12-25 Endurance
25+ Might as well do cardio
This is based on some science. Doing heavy singles/doubles/triples has been shown to increase maximal strength by increasing coordination both within a muscle and between muscles.
When discussing growth, it is important to get some higher rep work, and TUT also becomes an important factor because more volume generally means more growth. Although with growth it's not so cut and dry, as evidenced by this board and the fact that people get big doing a variety of work. One reason for recommending higher reps for growth could be that with higher reps (8+), you're not so much struggling just to get out the reps, so you can concentrate on controlling the negative, which is important for growth.
I try and think of it like this: if the weight's heavier than one you've touched in the recent past, it'll cause growth as long as you're lifting with reasonable volume (at least like 10 reps total). Eg, doing one single 1RM as a workset probably won't do much for ya.