It used to be we thought of just apoptosis and necrosis, with apoptosis being a clean and deliberate suicide, while necrosis was a messy and uncontrolled cell death.

While those are still very valid, it's turning out that there are a lot more ways for cells to die.

There's necroptosis which is controlled like apoptosis, but messy like necrosis. There's ferroptosis which is iron-reliant and happens in response to excessive oxidation. There's anoikis, which is very similar to apoptosis but initiated by lack of contact to extracellular matrix. There's NETosis, where a type of immune cell called neutrophils eject their DNA as a sticky net to capture pathogens. There's pyroptosis which is triggered by the inflammasome and strongly stimulates inflammation to combat mainly intracellular pathogens.

There are a few more I've left out, probably a few more I haven't heard of, and then all the ones we might not have discovered/characterized yet.