Strenght training mainly trains your CNS for efficiency and maximal fiber recruitment to perform a lift. As you get stronger your miscle cross section increases and your muscle does indeed seem to become denser.
Hypetrophy training differs in that you concentrate more on how you lift your weight, meaning that you concentrate on your muscle contraction as you lift the weight. Your goal at that point is to stimulate and exhaust the muscle. By exhaust i don’t mean failure just wearing it down with higher reps and more training variety.
I feel that both phases are to be used, when you come off a strenght routine and switch to hypetrophy program you grow very quickly for a few weeks.
The difference can be determined by looking at Volume of Work (reps and sets), Intensity of Work (load), and Frequency of movement. I would recommend reading Locked and Loaded by CT and the Set-Rep Bible by CW.