Indeed, that way my hoity toity Imperial/Altmer can look down with disdain as the "lesser races" trod through the mud. I love me some Altmer, so obnoxious.
Heres what I'm thinking the coach is for nobility while 'the cart' is like TARC in the cities only its fast and dangerous. The cart is cheap and decently fast but their is a chance of being robbed by highwaymen, bandits, or hell the cart owner might be in cohoots with the bandits and drive you all off the road to be robbed.
It may be more convenient much mre dangerous. Also in The Cart you meet many 'interesting' people, gamblers, brawlers, unlucky passengers, and many other pariah. The Cart is for quick cheap travel for most people, people are huddled up in a small cart with a thin canvas over their heads and hay seating. This method of travel is used by many poor, or people trying to find the quickest way out of town due to their history or debts.
Randoms events include-well if their were-
Bandits -always kill you
Highwayman- just rob you won't kill you if you pay.
Cart tips over from taking a sharp turn, some people may be dead or injured, you might get injured less your endurance and agility are high enough.
(good chance to feel around the dead passengers pockets)
Corrupt cart driver leads you off to some bandits.
Wild animals
etc
The wagon could just be a merchant convoy your traveling with, its the slowest but the safest and costs medium price. You may or may not have to help with the carts/food/ or gaurd on the way. Its the slowest but genuinely the safest. As long as you have a good reason or good mercantile and speech skills you can skip out on work.
Coach is a good speed and always goes the safest roads but pays the highest but more luxorious. Don't lift a finger and take a nap.
Maybe a bit to detailed for a FT system but I like details.