The traditional focuses of sociology include social stratification, social class, social mobility, religion, secularization, law, sexuality and deviance.
These were called calceus mulleus, and the name may have been shortened to mules by English speakers. Hence the primary difference between mules and clogs in early days was that clogs were likely to be worn by working people, and mules were fancier and favored by the aristocracy.
I have yet to see the difference between clogs and mules defined with regards to their shoes. Note: Some of the shoes labeled as mules actually have a lip in the back, although it does not go up the entire back of the foot's heel.