The Webster's dictionary says: Analogous (biol.) similar in function though differing in structure
Ana-Logos = according to the Logos (logic, ratio, principle, word).
Middle English analogie, from Old French, from Latin analogia, from Greek analogiā, from analogos, proportionate.
Metamorphosis is a Greek word; Greek is the source of an amazing number of prefixes and roots in English and other languages. It comes from "meta", meaning beyond, and "morphe", meaning form.
The word "analog" originates from the Greek word "analogos," which means "proportional." It entered the English language in the early 19th century and has come to describe systems or devices that represent or operate by means of continuous, varying quantities or signals, as opposed to digital systems that use discrete, binary values.