What is the difference between a caliope, a merry-go-round and a carousel?

Merry-go-Round vs Carousel - the difference is the direction they turn.

In the UK and Europe, merry-go-rounds (as they are most often referred to in those countries) usually turn clockwise (see photograph at top), while in North America, carousels typically go anti-clockwise (or "counter-clockwise"). One mounts a real horse by lifting one's right leg over the animal's back as it stands with its head towards one's left (the horse's left side is called its "near" side). Likewise for a carousel that turns anti-clockwise: one stands on the near side of the horse to mount (towards the center of the carousel, not on its outer edge). One possible reason for carousels in the USA turning anti-clockwise may be so that the rider can use their right hand to catch a brass ring.

https://en.wikipedia.org/wiki/Carousel

A caliope is a musical 'instrument' that is sometimes housed within a carousel.

https://en.wikipedia.org/wiki/Calliope_%28music%29