Why would a provider forbid tethering? And besides the why, how would they even know you're doing that? If I turn on my phones hotspot, doesn't that look exactly like my phone is doing something™ requiring a high bandwidth?
Very annoyingly, the iPhone also has a way for the carrier to somehow disable the mobile hotspot feature of the phone for their sim.
On the mobile hotspot settings page it will just show a message with a link to the carriers website instead of the toggle to enable it, I find it really annoying since as you said I don't understand how there would be a difference in what the usage would look like to the carrier and it feels like Apple is imposing a restriction just for the benefit of the carrier that makes the phone less usable.
Because they want to charge you for the expensive "tethering" option. I know, that's fucked up but the US are not very good at forcing consumer-friendliness on their companies.
On the "how they detect it", unless you're using a VPN they can look at the traffic and easy distinguish "computer traffic" from regular "phone traffic".