Full-time RV'er here. We have different classes of recreational vehicles (RV's) here in America. They are classified in two types with sub-types in those types. This may help you out...

• Motorized - There are RV's that have their own drive train and are drivable units. Many folks that have these also tow a small car, or jeep, behind them. This small car allows them the ability to get around town once their RV is setup at a campsite. There are 4 classes in this type.
• Class A - These are large motorized RV's that look a bit like a bus. There are a few smaller ones but they mostly will be in the 35 foot and larger range.
• Class B - These are the smallest of the motorized RV's and are built on a van chassis. Something like a Mercedes Sprinter van. The advantage of these is that they are small and maneuverable. You can go anywhere and basically camp anywhere, even in a parking lot. The disadvantage is a small living space.
• Class C - These are somewhere in the middle of the class A and class B. They are also built on a van chassis but the driving area is the only thing that will resemble a van. The back part of the RV is purpose built as a living space. Most of the RV's that you can rent in the US are these types of RV. They are a good general purpose RV that's easy to drive and still gives you a decent living space.
• Class Super C - There are as big as a class A but look a little different. They are built on a heavy duty truck chassis (Mostly Freightliner) and they excel at carrying heavy loads. They have huge towing capacity so many times you'll find them towing large trailers with additional vehicles inside.
• Towables - These are RV's that you tow behind a truck. Most are towed with a pickup truck but some folks tow with a heavy duty truck. The advantage to these is that once you unhook from the trailer you have your truck to drive around town. They come in 3 different types.
• Travel Trailer - Sometimes known as a "Bumper Pull" because these trailers connect to the truck from a hitch that extends from the back bumper area. They can vary in size from a small teardrop trailer to a 40 foot trailer. Because they connect to a bumper hitch they allow you have the bed of your truck free for any additional cargo.
• 5th Wheel - These connect to a 5th wheel hitch that lives in the back of the truck, hence the name 5th wheel (Although now a days a gooseneck hitch is also used.) You'll know a 5th wheel from the way it looks when it's towed. The front part of the trailer rides over the bed of the truck. They tend to be larger and taller than the travel trailers. The high ceilings in then make them feel much more residential. They also tend to have more storage on them since you're giving up the bed of your truck when towing them. This is the type of RV that my wife and I live and travel in.
• Toy Hauler - These come in both Travel Trailer and 5th Wheel configurations. The differentiator is that the back section of these will be a garage space. That space is intended to cary motorcycles or side by sides (Small dune buggy.) The living space is smaller to accommodate for the garage space. People also buy these and convert that grade space into different things. Many remote workers use it as an office space. Younger folks traveling with kids make it into a kids room/play room.

Since you're coming from Europe what you know as a "Caravan" is going to be most closely related to a motorized Class B or Class C, or a Travel Trailer when it comes to towables. There are a few nationwide companies that rent RV's so that may be an option for you. While we have never rented, the two we see all the time are Cruise America and Indie Campers.

Good luck on your hunt for a rig to travel in. If you have other questions about RVing in the US feel free to reach out. It's been our daily life for 4 years now and we love doing it.