What is the difference in types of curry?
The first thing you should do is get a Thai cookbook. Or at least look at one. They usually contain a section of recipes for the various curry pastes. You can see from the ingredient lists what they contain.
Differences in heat and taste really depend on the individual curry and on the ingredients used. Green Thai curry tends to be quite hot, but the comparison really depends on the heat and amount of the green chilies, the heat and amount of the red chilies in a red curry (if you're comparing), the amount of coconut milk used in the final dish, etc.
The best thing I'd suggest is to try them all. Either buy the decent ones in the cans, or make them yourself if you're ambitious. Then you'll soon be able to answer your own question!
It has been a while since I squinted to look at the labels on the small cans of Thai curries that I prefer. The label listing is helpful in answering your question but probably not sufficient to derive the recipe. Massamun is going to have more cardamom and cinnamon - maybe clove(?). It is closer to an India/So Asian curry.
In 20 years of dabbling, I have not figured out how to make the perfect Vietnamese yellow curry. Maybe it is because I start with the cans of curry paste. There are Thai cookbooks that spell out the details curry paste recipe in the kind of detail your aunt shared with you - it might refresh your memory. I'm sorry I don't have specific references, I work from my own tattered notes.
I asked my aunt that question once. She said that the green curry uses fresh herbs and spices whereas the red curry uses dried. She taught me how to make green curry paste from scratch once, but I should've written it down. That's the best of my curry knowledge, don't know much about the other types.