There are four terminologies as follows -
Paleontology - study of fossil remains, paleontologists are people who actively excavate fossils as part of their job. Generally this requires a decent amount of training in geology and biology.
Paleobiology - Paleobiology is really more limited to the study of the biology of extinct animals, and they tend to study specimens in museums more so than excavate them.
Paleoanthropology - Paleontologists and paleobiologists generally call folks who study fossil hominids (our ancestors and closest relatives) paleoanthropologists (anthropology is the study of humans). This can be considered a "subset" of paleobiology or paleontology of course.
Paleozoology: Generally, people who describe themselves as paleozoologists tend to be interested in identifying species, naming them etc .