First and foremost please don't anybody take this post personally.  I'm not targeting anyone and I'm not at all trying to be snarky.  I'm asking an legitimate question because I honestly don't know the answer.

On a large number of occasions I hear people say they lift heavy while cutting, why?  You obviously have to be in a caloric deficit when cutting and lifting heavy seems like it would be geared more toward building muscle.  Those two at the same time seem like a contradiction.  Also, if you specify you lift heavy while cutting, what do you do when you're bulking?  That seems like it would be the more logical time to lift heavy.  When cutting I'd think you'd want to use a slightly higher rep range.  What am I not understanding?

Always lift heavy. Build muscle while bulking, retain muscle while cutting.

Volume vs. Intensity

Oversimplified, volume pushes hypertrophy.  Multiple sets of 8, 10, 12, 20 reps done at 50, 60, maybe 70% of your 1 rep max.

Intensity is a percentage of your 1 rep max.  High intensity, or "lifting heavy" is sets of 5, 3, 2, or single reps done at 80%, 90%, or at max.  This is what builds strength or "power."

This is why, generally, it's easier to lift "heavy" while on a cut.  3 sets of 10 @ 70% (30 reps) affects the body differently than 3 sets of 5 at 85% (15 reps).

Gotcha.  Thanks

The sad news is that it looks as though I've been doing it wrong for 25 years.  I've been doing high intensity (Mike Mentzer/Dorian Yates) work outs since day one.

Those guys are body builders right, they care about size, proportion and symmetry.  What were their workouts?

It's not like doing sets of 12 won't make you stronger.  Nor will only doing 3x5 not make you bigger, kinda depends on intake, but, doing the exact same thing for years probably didn't net much.

I'm talking mostly about weightlifting, but the programming can be applied to strongman or powerlifting; it's just periodization.

12-15+ weeks to reach a certain goal at a specific time.  First weeks will be high volume, increasing intensity with a lot of exercise variation, point being hypertrophy.  Then they'll lower volume but increase intensity with a limited number of exercises.

The last few weeks will be spent peaking for the event.  Very low volume, very high intensity, very specific exercises.

I've always been more interested in hypertrophy than strength.  Which, based on your input, tells me I've been doing it wrong.  I liked the Mentzer/Yates philosophies partly because I hate doing high rep sets.  It's a mental deficiency on my part.  I can push myself to physical failure with sets of <10 reps.  More than that my brain usually gives out before my muscles. That's especially true for squats.

Correct.

I've done both and had much more success at maintaining strength when I lifted heavy with long rests between sets.

I tried a hybrid lift heavy with short rests and it didn't maintain as well either.