Pumas are part of the felidae family:
Pretty tricky to follow the sub-family and decide what is and isn’t a puma from there on.
Genus Clarification From Quora:
puma concolor concolor
puma concolor couguar
Cougar, Mountain Lion, and Puma are all one and the same. They reside in North and South America.
Also interesting sub-note on the Panther:
Panther is a name commonly used to identify with a big, black cat. There is no separate species of ONLY big black cats in the world, however, there is a recessive gene found in both Leopards, and Jaguars, which occasionally causes Melanism, wherein a cub is born with what appears to be black fur. This is fairly rare, but the general public predominately refers to these black cats in both species as Panthers.
Documentary and Book on North American Pumas:
“We don’t realize the pumas are there but they are.”