The difference between primates and hominids: a primate refers to members of the ORDER Primate which includes monkeys, lemurs and apes. A hominid is a member of the FAMILY Hominidae (great apes) which includes gorillas, chimpanzees, orangutans, and us humans. A hominid is just a specific group of primate. Meaning, since the order primate composes of monkeys, lemurs and apes, the hominid is just a certain kind of primate belonging to the "ape" category, which differentiates it from other primates who belong to the "monkey" or "lemur" subtype.
I hope this helps.