HEAT stands for High-Explosive (or High Energy, whichever) Anti-Tank. It's pretty much a shaped-charge inside a tank shell. It tends to have a lower penetration other shells, but the thing is, it KEEPS it's penetrative and explosive properties over distance. It's effective against solid steel armor. I think a Chinese tank with an 85mm main gun had a HEAT shell that penetrated 800mm (yes, eight hundred) of steel. Good lord. And if it penetrates, it also showers the crew inside with molten copper.

And with that high-explosive part, it can also take care of squishy targets like infantry and jeeps easily.
ATFSDS, SABOT, etc. is pretty much solely anti-tank. It's a super-fast shell made of a REALLY hard metal, so it pretty much penetrates anything with brute force. Something that weighs a lot and has high speed, according to Newton, won't stop very easily. And any armor, including chobham armor (the ceramic armor that modern tanks use), have a hard time stopping that.