You can have a lambda calculus, the calculus of the real numbers or a logical calculus but on the other hand you could also have an algebra of sets, a Lie algebra, or a linear algebra.
Is there any convention which dictates whether something is an algebra or a calculus?
From my understanding, a calculus seems to give you information about objects you might encounter within a space, while an algebra gives you information about the interactions and structure within the space as a whole. Is this correct?
A calculus is a system of rules for manipulating symbols and expressions. An algebra is a set with operations that can be preformed on its elements.