The term "panther" is considered synonymous with the leopard, Panthera pardus, of which there are nine sub-species. Although the term "panther" is most tightly associated with melanistic leopards, the word is also applied to several different species, including the cougar and jaguar, when they display all-black coloration.
Panther is a somewhat antiquated term for leopards and other big cats, and it has fallen out of favor in the scientific community since the 1960s. The so-called black panther is not a separate species of cat, as is often supposed. It is simply any large wild cat with a condition called melanism, which causes its fur to become overly pigmented. Although leopards are the species most closely associated with this coloration, jaguars are also sometimes melanistic, in which case they are called black panthers. If jaguars are included as panthers, there are 12 living species of panther as of 2015.
Both jaguars and leopards belong to the genus Panthera, which also includes lions and tigers. The cougar, which is also sometimes called a panther, especially when it has black coloration, is not a member of that genus at all and does not closely resemble jaguars or leopards in its normally colored form. Cougars have a multitude of common names, including "puma" and "mountain lion," which adds to the confusion.