How does data transmission through coax and twisted pair differ?

I think of coax as basically radio waves contained within the outer shielding, kind of like how fiber-optic is light contained within glass. And the copper core is what generates the waves along the way, almost like a really long antenna. Is that a correct analogy?

I think of twisted pair -- Ethernet, USB, etc. as fundamentally different. They generate RF and can be affected by it (despite the twisting), but that's not what they use to communicate, instead they use voltage drops (electrical pulses) to simulate 1s and 0s. And this is why a coax signal needs a modem to convert the RF analog waves to digital pulses, and twisted pair or fiber optic cables don't because it's already "digital" pulses of either light or voltage.

Am I correct in my assumptions so far?

Where I get confused is that coax and twisted pair are still fundamentally copper electrical cables, yet I think of coax as RF and of twisted pair as using electrical pulses (and not wanting to have anything to do with RF). To further complicate things, is Wi-Fi then basically the same as coax, except the waves aren't contained within a cable? And does that mean that a wireless AP is a modem of sorts?