What is called the "area size that an animal usually lives in"?
Are you looking for 'Home range' (see also the definition in Encyclopaedia Britannica)? Generally, 'home range' is defined as the entire area an individual animal uses, while the 'territory' is the subset of the home range that is actually defended from conspecifics (in animals that show territoriality). 'Home range' is often delimited by the types of environments used and movement patterns of individuals.