You are correct. usbc is backwards compatible, but does have additional protocols for better charging. In fact, an old brick might not charge your new phone well, although the interface works. Newer phones might use power barely faster than the brick can provide. Try Charging a Note 20 with an old brick overnight....
For example, there is an entire handshake that happens over usbc that can say "can I do 10v" or "I can do 15v". An 80-watt USBC charger can potentially charge your phone in 5 minutes to full charge, but there is additional circuitry to implement the USB Power Delivery specification.
USB-C is superior to lightning in every category. Apple is going to drop lightning soon, and this makes sure they stay on a standards track.

https://www.lifewire.com/usb-c-vs-lightning-5206813