Basically, Necrosis is like an atomic bomb going off in the cell where as apoptosis is a more controlled regulated process. Important to remember about apoptosis is the pathway involved to stimulate the cell the go through apoptosis. There are two pathways, intrinsic and extrinsic. The extrinsic apoptosis pathway is involves the binding of the Fas ligand to the Fas receptor resulting in a cell signalling that causes a clustering of the Fas receptors. The clustering of the Fas receptors recuits FADD and pro-caspase 8. The pro-caspase is a pro-enzyme, similar to your tryposinogen going to trypsin. When your pro-caspase 8 is activated to caspase 8 through autocatalysis, it will then activate pro caspase 3. It is the caspase 3 that will initiate apoptosis.
Then there is the intrinsic pathway that is a little more tricky. This is usually caused by some internal damage from the mitochondria. When mitochondria is damaged, it will release cytochrome C. This is easy to remember because your Cytochrome C is important in the electron transport chain. It can either be oxidized or reduced as the electrons are being bounced around to the final electron acceptor, oxygen. So the mitochondria releases cytochrome C from the internal mitochondrial membrane. Cytochrome c, released from damaged mitochondria, binds Apaf1, which then activates an initiator caspase, in this case caspase 9, which then activates the effector caspase, caspase 3.
There is also a Bax protein that can be signalled to go into the mitochondria and cause it to start releasing all this stuff as well. When studying this stuff it is important to know just know what the stuff means, but to go into all these detail so that you can fully comprehend apoptosis and necrosis. The difference between apoptosis and necrosis will be like 1 question on the test whereas this whole pathway will be 5-6 questions.