niothing
No, the relationship between moth and sloth is not parasitism. The moth benefits from the nutrients on the sloth's fur, while the sloth may benefit from the moth's presence by gaining protection from predators. This relationship is more of a mutualistic symbiosis.
yucca moth
There are three main types of symbiotic relationships: mutualism, where both species benefit; commensalism, where one species benefits and the other is unaffected; and parasitism, where one species benefits at the expense of the other.
The moth will live in the fur of the sloth until it is time to lay it's eggs. Once a week the sloth goes to the bottom of the tree to lay it's waste. The moth then flies onto the waste and lays it's eggs. After all that the moth hitches a ride on the moth to live the rest of its life.
It is a moth, known colloquially as a "Yucca Moth"; scientifically "Prodoxidae". I very recently watched David Attenborough's 'Life on Earth' series where this symbiotic relationship was featured.
sloth, moth, cloth, broth
cloths, moths, troths
The Yucca Moth lives in the southwestern United States, Mexico, and the West Indes. Yucca Moths have a symbiotic relationship with the Yucca plant, they can not exist without each other.
The moth you have found is a Luna moth.
Three examples are Horse, Hippopotamus, Hyena, and there are many more.
The kind of moth that has black and white wings is called a "panda moth."
The moth that has circles on its wings is called the "Luna moth."