The characteristic roar, typically heard from tigers and African lions and jaguars is not possible for the cougar to produce from its larynx, or voice box. This is because of the structure of the hyoid bone, in the animal's throat that is connected to the larynx. The cougar's hyoid bone is not equipped to roar because it is not big enough. That is why the mountain lion is grouped with the house cat, in the Felis genus. Needless to say, it is the largest species in the genus.
Cougars do make a very distinguishable noise, much different from a roar.
It is described in Young's book, the Mysterious American Cat, as a sort of scream. This scream can be heard up to two miles away in an open area. It is such a high pitched noise, that even though it may not initially be as loud as a roar decibel-wise, the sound travels much further. The cougar also purrs, as common with all cats, and has a variety of maternal calls as well as basic communications between mating adults, rival males, etc. Naturalists call the male pumas tomcats.