I'm interested in the math and physics of the whole thing.
I find it simplest to consider that there are two aspects of cylinders, with no difference due to tank material (steel vs. aluminum): the force gravity imparts (i.e., dry weight) and the buoyant force.
The buoyant force is simply due to the volume (shape). If you fill a bathtub to the rim, then put your tank in the tub and push it down until it's just completely submerged, a) you'll make a mess on the floor, but b) the weight of the water (# of pounds) that was displaced (onto the floor) equals the buoyant force.
When diving, the difference between dry weight (W) and buoyant force (B) is what matters. If B is more than W, the object floats. It's not just limited to the tank, though. The exact same principle applies for you, your torch, your drysuit, etc. The bottom line is the TOTAL volume vs. the TOTAL weight (dry). For an AL80 tank, it turns out that the buoyant force is larger than its weight. However, it's not worth getting caught up on that any more than you worry about whether your body displaces more water than it is heavy.
Unsurprisingly, most people use the word "buoyancy" to be that bottom-line, net difference between total weight and total buoyant force.
If the net buoyancy is positive (buoyant force larger than weight), then you need to change that to be neutral. Adding lead increases both weight and buoyant force: weight by a lot and buoyant force by a little. The net result is the balance shifts toward the "weight" side, reducing buoyancy.
Switching out an aluminum tank for a steel tank (of comparable gas capacity): weight goes up and buoyant force goes down. Both serve to reduce buoyancy. A high-pressure steel more so than a low-pressure steel. If you were too buoyant before, you'll be better now. If you were already neutral (or even negative) before, you're going to be worse now. In the latter case, you'd need to add buoyancy back in -- as you might expect, reducing the amount of lead is an easy way to do that.
So choice of tank vs. lead act the same with regard to total buoyancy (whether you sink or rise). One major reason people use steel tanks, though, is that it distributes the weight higher on the body, affecting TRIM (whether you rotate). (Same thing with stainless steel backplates.) People that use aluminum tanks very often need to put some of their lead on a tank band or trim pockets. They don't carry MORE weight (as that would impact buoyancy), they just change where it's positioned.
Hope it helps!