In 1985 Luca Cardelli and Peter Wegner, my advisor, published an ACM Computing Surveys paper called “On understanding types, data abstraction, and polymorphism”. Their work kicked off a flood of research on semantics and type theory for object-oriented programming, which continues to this day. Despite 25 years of research, there is still widespread confusion about the two forms of data abstraction, abstract data types and objects. This essay attempts to explain the differences and also why the differences matter.