The reason is twofold. This famous wild cat species has a very wide distribution across the Americas although it is shrinking. Also, it has been recognised and recorded for many hundreds of years which has given widely disparate races and peoples time to write about it in their own way. The first reason is the more important.
Distribution
Historically, the distribution of this wild cat species was enormous. “The cat was found from Northern British Columbia across the southern portions of the Canadian provinces to New Brunswick, south through all of the United States, through Central America, and into South America to the tip of Chile” (SP Young and EA Goldman in The puma, mysterious American cat – 1946). The geographic range is the largest any terrestrial mammal in the Western hemisphere. Nowadays you may know that pumas have been extirpated from the eastern United States. This occurred by the late 1890s. There is a small population in southern Florida.
Across this huge range different peoples gave different names to the cat. I have a page on the various names of the species of cat and therefore I won’t repeat that article here. Please click on this link to read it.
Timeframe
In 1609, the name “puma” first appeared when Garcilasso de la Vega, the son of a Spanish conquistador and an Incan Princess wrote: “lions are met with, though they are not so large and also fierce as those of Africa. The Indians called them puma”. Christopher Columbus (1451-1506) was one of the first to call the cat a “lion” because the it resembled the African lion.
Scientific and popular
In South America, today, the cat is normally called puma subject to a range of local, regional names. In North America, the scientific community use the word “puma” while the public prefer “mountain lion” or “cougar”. Its scientific name, Puma concolor, was created in 1771 by a Swedish botanist, zoologist and physician, Carl Linnaeus (1707-1778). The name “lion” (león) is used widely in South and Central America. In Brazil it is called leão.
“Predatory” older women
Society has adopted the word “cougar” to describe an older heterosexual woman who pursues sexual relationships with men who are younger. The pursuit of men hints at a predatory nature hence the description.