Question here. I don't know of any phaetons that are not 4-wheel vehicles. While all carts only have 2-wheels.
So my question is do you want a 4-wheeled carriage or a road cart with only 2 wheels?
Many vehicles have been misnamed, wrong names applied or names have been twisted over time so they are changed into unrecognizable descriptions. Same vehicle is called one thing in the East, totally different name in the Midwest.
Do you have a photo of a vehicle LIKE the one you want to buy? That would probably be the most helpful for us to aid you with finding a vehicle.
And sorry but you have to go private about selling stuff or the Moderators will get after you.