What's actually the difference between a study permit extension and a whole new application?

If you're still enrolled in the same or a similar program, you extend/renew (apply to "extend or change conditions") rather than starting a brand-new study permit application from scratch — you'll want to apply well before the current one expires so you stay in maintained status if there's a processing gap. Talk to your school's international student office too, they've usually seen your exact scenario before.