What is the difference between missing completely at random and missing at random?

The terminology describing missingness mechanisms is confusing. In particular the meaning of 'missing at random' is often misunderstood, leading researchers faced with missing data problems away from multiple imputation, a method with considerable advantages. The purpose of this article is to clarify how 'missing at random' differs from 'missing completely at random' via an imagined dialogue between a clinical researcher and statistician.