What is the difference between lifting and lifting heavy?

Pretty much. Heavy is relative to your strength. I see the best results in body comp and strength when I lift 5x5 (5 sets of 5 reps, heavy enough that I really struggle on the last rep) for the big lifts. For some accessory lifts, I still do 10-12.

I had pretty decent results when I was lifting everything in the 10-12 rep range too, though. Any resistance work is better than none.