Hyenas, mongooses, and civets are feliforms, but not felids or felines.
Lions, tigers and leopards are feliforms and also felids, but not felines.
Cheetahs, cougars, and domestic cats are all feliforms, felids, and felines.
There's a similar distinction between "caniform," canid," and "canine" for the "doglike" carnivores. Bears are caniforms; fennec foxes are both caniforms and canids; wolves are caniforms, canids and canines.
And between "hominoid," "hominid," "hominine", and "hominin" for the "humanlike" primates, i.e. the apes. Gibbons are hominoids; gorillas and orangutans are both hominoids and hominids; chimpanzees are hominoids, hominids, and hominines; Lucy is a hominoid, hominid, hominine and hominin.
Of course, reality is more complicated than human language, and we run out of words long before we've named every evolutionary group at every level. But that's why we invented cladistics!