ok me and my dad have been having a huge argument. he is saying that a mountain lion(cougar) is a type of lion. But i say that a lion and a mountain lion are not the same and that they are different species from the cat family. he is basically saying a mountain lion is another name for a lion, when i know from research that a lion is from a different group then a mountain lion. who is correct?

Well this is the problem of using common names instead of scientific ones. The lion goes by the scientific name Panthera leo but 'lion' is a common suffix for a variety of common names for larger cats (in the same way that 'panther' is also used).

Obviously the mountain lion (also called a cougar and puma to add to the confusion, this is why scientists like Latin names, it avoid confusion) is a fairly close relative of lions - it is a large bodied cat, but is in a different genus to the lion (Puma concolor). The closest relatives of the lion are also in the genus Panthera (P. onca - the jaguar, P.tigris, the tiger and P. pardus, the leopard). As such while the mountain lion is a close relative of the lion, it is not the closest realtive of the lion, P. leo.

They are not the same species or even in the same genus and so are different animals. That makes you right, but break it nicely to your dad! It's easy to get confused with these names and they do look similar.

To add to Dave's answer, the Lion belongs to a group of cats typically called the pantherines or Great Cats (or Great Roaring Cats) which includes the genera Panthera and Neofelis (Clouded Leopard) (although Neofelis doesn't roar).

The "mountain lion" (Puma concolor) on the other hand belongs to the genus Puma and is a close relative of the Jaguarundi (Puma yagouaroundi) and believe it or not the Cheetah (Acinonyx jubatus).  The relationship of this "Puma" (Puma+Acinonyx) group with the "Panthera" group can be a bit controversial depending on the study you chose to believe but a recent comprehensive molecular study would indicate that these two groups are actually quite distant, with the "Puma" group being more closely related to the other small- to medium-sized cats and in particular the "Domestic Cat" group.