Yes, but they're not mutually exclusive.
ol' Zir Red posted a research article a while back that showed that stimulating growth can occur at nearly any rep range. what matters is similar to what arnold said in pumping iron. all the reps that lead up to the last rep are worthless. it is that last rep in the tank that pushes the stimulus for growth. whether that be the 5th rep, 10th rep, or 20th rep. push it hard till the end.
we also know that lower reps help more so with improving your efficiency, or improving strength. so you can do both to some degree. just like the different energy systems of the body. you use them all, just at times you use 1 more so than others.
Pretty much these answers. I honestly think that size and strength are very closely correlated. Not between different people, but between different versions of yourself. For the most part, a stronger version of you will be a bigger version and a bigger version will be a stronger version.
Is this 100% true? No, it is not. You can gain strength for a little while by various mechanisms - the most obvious being neurological improvements. You simply get better at a movement, get better at firing more muscle fibers at once, etc. But this only goes so far. Maybe you will gain 5,10, even 30 pounds on an exercise (who really knows? I don't), but eventually you will require bigger, thicker fibers to support the weight and more material in the muscle to fuel contraction.
On the flip side, you can maybe train to improve the size of your muscle without gaining strength....but this will only go so far. Eventually you will be able to curl a weight 100 times and your body will no longer adapt because the stress is not sufficient to warrant any adaptation. Not to mention the amount of energy burned will hurt your body's ability to adapt.
IMO, the best way to increase size is to increase strength. Constant progress on strength will bring the size.
And just to point out, the two people I quoted often disagree with me on many things, and we've had many great discussions because of it. But it appears we agree on this, which has to mean something. The end of the world is near?