The main difference, or at least what I think I'm understanding is basically how you count the days. Ordinary interest assumes a 360-day year, so every month is treated like 30 days, while exact interest uses the actual number of days in the year, 365 (or 366 if it's a leap year). Same formula, just different "day math." (Cleaves, Cheryl, et al. Business Math. Sonoran Desert Institute. Pearson Education. 2023. Chapter 11. Pg.420)

Ordinary interest sticks around because it's easy and consistent. Back in the day, 30-day months and a 360-day year made calculations simple before calculators were a thing. Today, banks and lenders still use it for consistency across loans, bonds, and short-term money market stuff. I think I found that It's also slightly in their favor because it can push the effective yield up just a bit. I can't quote that part though because I cant find where I think I read that.

As for the last question, pretty much yes. Any time you knock down the principal before the due date, you reduce the interest that would have been charged on that money. Just like paying off a mortgage in 15 years instead of the normal 30. Ordinary vs. exact interest just changes the tiny details of how much you save, but the principle is the same. Get that principal down sooner, save some of your hard-earned money. The only thing that could mess with that is prepayment rules or penalties in the loan itself, so I think it would be a good idea to check how extra payments get applied.

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