The clocks are the same, except the ones known as
carriage clocks featured a handle on top, and were originally used as travel clocks. These clocks often sit on mantles, a shelf that projects from a wall above a fireplace.

See source for pictures of mantle clocks with and without handles.

carriage clocks are a style of mantle clock they just have a handle. they were designed to travel in the early days by a large handle and glass door to protect the face of the clock