My answer comes
from Kinesiologic data that was measured when the exercises were done correctly. If that makes it complicated, and if that's what was referred to above as complicated, then that's life.
And MY experience is that I feel the glutes more when doing lunges. How the user does the moves has something to do with it as well. If you have knee pain doing lunges, then one should check where the knee ends up on the lead leg during a forward lunge. The knee should never go past the foot. If it does, then you need to make the step forward bigger, AND, this will naturally engage the glutes more and lessen the chance for knee problems with lunges.
Bottom line, they work basically the same muscles. The intensities differ with these two exercises....basic moves tend to give more absolute intensity and aux moves tend to be more relative. You can go heavier with squats as well, which is why the protocol is usually squats as a basic move, lunges as an auxiliary exercise.
One other thing, I DO NOT recommend shoving anything under your feet, such as boards or dumbbells, when doing lunges or squats. That's a very dangerous thing to do IMHO.
T.