Lifting heavy is the best way to add strength. Doing lots of reps with less weight (more volume less intensity) gives you more mass (hypertrophy) (the old beach muscles)
Respectfully disagree. Look at the strength and muscle mass of weightlifters and those World's Strongest Man guys. I have always trained as heavy as possible in the 6-10 rep range. Doing so, from the age of 19 until age 44, I went from 155 to 220 relatively lean pounds, consuming at least a gram of protein per kilogram a day, in the form of lean meat/fish, yogurt/kefir, as well as protein shakes (in smoothie with berries and oatmeal at breakfast, one post-workout). Supplements were pretty much limited to a multivitamin and a testosterone booster (the legal ones you can get at GNC, etc). Rest is incredibly important, as is avoiding over-training. Diet and rest are perhaps more important than the workout itself. Ya gotta feed the beast, and let it recover.
Yes, he was full of 'roids, but Mike Mentzer was a strong advocate of the "Heavy Duty" training philosophy (btw - even on 'roids, you still have to put in a hell of a lot of work in the gym and the kitchen to look like a Mr. Olympia competitor). Many European classic-era bodybuilders (approximately '60s-'80s), like Germany's Jusup Wilkosz, began as competitive weightlifters, and it shows in the thickness of their bodies.
However - in the end, figure out what works best for your body, especially your metabolism. When I began my metabolism was freakishly high. The heavy weight/relatively low-rep approach worked well for me.