History of anthropology
The first use of the term "anthropology" in English to refer to a natural science of humanity was apparently in Richard Harvey's 1593 "Philadelphus, a defense of the legend of Brutus in British history", which, includes the passage: "Genealogy or issue which they had, Artes which they studied, Actes which they did. This part of History is named Anthropology."
Anthropogeny
The root in ancient Greek "anthropos" means human and "-logia" means discourse or study, and "wiktionary:-genesis" means the process of creation or origin.
"Anthropology", therefore, is quite literally the study of humans, whereas "anthropogeny" is the breakdown of the word anthropos agai but with the link word -geny (γένη, γένος) which again literally means the study of the birth and gender of humans.