Besides specific differences in chemical steps involved, the main difference between aerobic and anaerobic respiration is the terminal electron acceptor: oxygen for aerobic respiration and some other chemical (which is variable) for anaerobic respiration. This also leads to a difference in energy yield, since oxygen is a more effective acceptor, leading to more energy being extracted from a given starting material.
Work Step by Step
For this answer, review Concept 9.1 and note the main features of these two kinds of respiration. While there are differences in details, the overarching difference, which goes right to the purpose of respiration, has to do with energy extracted and the associated terminal electron acceptor.