A carriage is a vehicle with wheels that's usually pulled by horses. In some cities, you can go for a carriage ride through the park.
A carriage generally has four wheels and is pulled by two or more horses, while the smaller cart tends to have two wheels and be pulled by a single horse. In Britain, you might hear people refer to the separate compartments of a train as carriages as well, and in some parts of the US it's used to mean "baby stroller" or "grocery cart." The Latin root is carrum, "two-wheeled war chariot."