When do you call something "a calculus" vs. "a logic"?

The short answer is, after a few more months of letting this sit, is that in reality there is no difference between algebra, logic, and calculus. They are all just saying "a formal collection of mathematical rules". But each of these words have a history, and so when authors use them, they are mentally invoking that history of the word. Because these words were used in the development of different ideas, the logic/calculus/algebra typically prioritize different ideas.

It is like saying "what is the difference between book and tome"? They both are the exact same thing, you are just highlighting different aspects of it by invoking mental imagery. In the algebra/logic/calculus case, the mental imagery is the history of it's use.

I would elaborate on the answer above with respect to the etymology of logic. Logic is closely associated with philosophy since the days of Aristotle. Many philosophers are well-versed in logic, but not as something that you represent symbolically. This is what is known as informal logic and involves such things as logical fallacies and assessing the validity of an argument.

Then, at the very foundational level, we have the work of logicians like Frege, Russell, and Gödel, who saw logic as the foundation from which to derive arithmetic and thence, algebra and calculus. In this view, the difference between the terms it not only historical, but hierarchical as well.