Ok quick and dirty, any calibre can be explosive, you just put explosive in whatever calibre. .50 is the usual starting point, but it's not effective until 20mm or so, like said. DU is just a dense material, like lead is dense, so it retains velocity better than a light material in the face of air resistance (and armor resistance!). Tungsten is dense too, but it's generally inferior to DU, which means depleted Uranium, which should really just be called uranium 238. Uranium 235 is the stuff for making bombs, and they take as much as that out of the ore as they can get, like panning for gold. So DU is U238 and a smidgen of 235 and 234.
Anyway when talking armor penetration they use mm, just a standard thing. Besides that a 16 inch naval gun will pass through slightly more than 1.5 feet of armor. I think it'll pass through more than 1.5 meters of armor. Honestly it's hard to imagine what it wouldn't pass through. Incidentally, naval guns like WW2 shot bullets that were AP and HE, so they penetrate armor and also have explosive in them to blow up just after penetration.
When stuff hits other stuff at really fast speeds (or maybe just high pressures, not sure if time has anything to do with it) materials all seem to act like toothpaste. So when you shoot a .50 bullet at a steel plate the bullet erodes the steel, and the steel flows up around and behind the bullet. Then if it penetrates it can knock off a big chunk with it on the other side, or not, I guess it depends. Also this is how HEAT warheads work. They aren't really hot, though people say they make molten metal that melts through armor thats bull????. it's just a cone of explosive with a thin layer of metal inside it. The explosive detonates, and the thin layer of metal is forced, like toothpaste, into a couple thin steams that hit the armor and erode it. The fast stream of metal moves like 10 000 meters per second, or mach 30, so it's pretty fast - but it only holds together for short distances, less than a few meters. So you hit a piece of armor with a HEAT warhead and there will only be an itty bitty hole in the side, and maybe coming out the other side. And anyone inside is in the way of debris kicking in and out and around at high speeds.
So to stop HEAT warheads they use reactive armor blocks, which are square boxes with a metal tile sitting on some explosive. The HEAT jet hits the box, the explosive underneath the metal tile explodes, the metal tile flies up towards the HEAT stream, and the stream punches through the flying metal tile. However the stream is wobbly now because the tile messed it up, so it doesn't penetrate well when it hits the tank's armor. Also they use electric armor now that requires a lot of electricity, and it just vaporizes the HEAT metal stream with high current.
For AP shells the trick is to get velocity up there, faster and light is better than heavy and slow. So they used to make just ordinary bullet shapes out of steel, but those weren't good enough. So they worked on ways to increase the speed, and came up with a little ridge that runs around the bullet, and it makes the bullet fit into a larger diameter gun. This means the gun can put more pressure on the bullet, and it will go faster. Just before the bullet leaves the muzzle a constriction flattens out the ridge, and you have a smooth, fast bullet. This was just tricky to make, and expensive, so they gave up on it. So in WW2 tanks just shot each other with full-calibre steel projectiles, shaped like the top half of a rocket ship. Then they had problems with steel - it's light so air slows it down faster, and if it hits a really hard armor while it's moving fast it can just shatter on the spot. So they used Tungsten when they could get enough together, and it didn't have either trouble.
Still they had a good material, but they couldn't get the velocity high enough with the propellants they had. If they used any more powder the gun would explode, unless they used the previously mentioned squeeze-bores, and those wore out too fast. So they put a case around a projectile, like a cylinder of wood with a hole drilled down the middle, and then cut in half, and called it a shoe (sabot). They put the bullet in this sabot, and when it shoots down the gun thy can use a lot of powder in a big calibre gun, but when the projectile comes out the wood falls away and a small bullet is travelling very fast.
So they had bullets that are dense and very fast, but they still couldn't go through enough armor. They'd get stopped by 500mm or so. What they did was keep making the bullets longer, longer and longer, so they had a small front surface area but lots of weight on them they would retain velocity REALLY well. Then they found out that they made bullets so long that they couldn't spin them fast enough to keep them pointing forward, and they had to put fins, like on a dart, at the back of the projectile. This meant the bullet wouldn't spin (much) and they made the guns smooth-bore, and the projectiles a few feet long.
