Final answer:
The term for the study of language development and its variations is linguistics.
Step-by-step explanation:
The discipline of linguistics is devoted to the study of language. One subfield of linguistics, sociolinguistics, examines the social context of language use, such as how language varies according to age, gender, class, and race. Another subfield, linguistic anthropology, studies language as an aspect of larger cultural processes. Therefore, the term for the study of the development of language over time, including its changes and variations, is linguistics.