[lutusp]

> As an example case, why is relational algebra not called a calculus, and why is the π-calculus not called an algebra?

Because algebra and calculus are defined differently.

> The principles of calculus, historically, are differentials and integrals, while those of algebra are operators and equation solving.

Yes, and this leads me to wonder why you asked.

> Contemporary principles are analysis and abstract objects, respectively.

There are many fields that have some elements in common, but that are sufficiently distinct to merit different names and definitions.