Good answer. It should also be noted that it depends on the ratio of type 1 and type II fibers of the individual. If you don't have a lot of Fast twitch muscle fiber, the heavy lifting won't be as effective. This is what leads to endless arguments as to what kind of training is best. What's best is a combination on heavy low rep and "pump" style training empahasizing what you resond best to.
Increased strength just ALLOWS for more stress on the muscles which in turn leads to more muscle growth. So they're related but not necessarily contingent on one or the other. You can get much stronger and not get much more muscular.
Old time legend Sig Klein said: Train for beauty and strength will follow. That's inevitable. But the strength increase may not be extrodinary. It depends on what's more important to you. This leads to a hypothetical question that I'll ask in another thread.