They are distant relatives. The closest relative of the jaguar is the lion. The jaguar probably evolved from the American subspecies of the lion before the end of the last ice age. Lions live in savanna type habitats, but jaguars prefer forests. The spots on a jaguar allows it to hide inside a forest. The next closest relatives of the jaguar are the other roaring cats, such as the leopard, tiger, and the snow leopard. The closest relative of the roaring cats is the clouded leopard of Asia. The clouded leopard probably evolved from an Asiatic linsang. The clouded leopard is regarded as the most primitive cat, and all other kinds of cats, both large and small, roaring or not roaring most likely evolved from the clouded leopard, which is a medium sized cat that climbs trees.
House cats belong to the group of cats that cannot roar, but they can purr (the roaring cats cannot meow or purr). The cougar and the cheetah are big cats, but they are more closely related to the house cat than they are to the roaring cats. The cougar and the cheetah cannot roar, because the hyoid bone of the roaring cats has migrated down their throats. House cats evolved from the African wildcat (scientific name is Felis sylvestris libycus), when the African wildcat was domesticated by people in the middle east shortly after agriculture was invented after the end of the last ice age.