Aren’t those synonyms? Just before the arrival of the first actual programmable computers, the word was a job description for people who did calculations.

From https://www.etymonline.com/word/computer

“Earlier words for "one who calculates" include computator (c. 1600), from Latin computator; computist (late 14c.) "one skilled in calendrical or chronological reckoning."”

The Antikythera mechanism can definitely do that.

I would argue that in modern parlance no they are not. We could pick multiple examples of things doing calculations, like cash registers. They sum up numbers. Clearly they do calculations. But are they computers?

Even now, would you say the type of cash registers where numbers are manually entered are computers?

A classical cash register is not the same like the thing we call computer, but that's not my point. My point was that "a computer is a thing that computes while a calculator is a thing that calculates" does not sound correct, the argument is basically the wrong way around. In my opinion, the verbs "to compute" and "to calculate" are synonyms. We only recently started to distinguish between a computer and a calculator, probably being a bit fuzzy and sloppy regarding the term "computer" (as natural languages are). But that doesn't mean that we can transfer that implicit (and maybe altered) meaning back to the verb "to compute".

In Greek, my maternal language, both are called "computers". A calculator is specifically a "κομπιουτεράκι", or small computer, whereas "computer" is "υπολογιστής", literally, "calculator".

In English also the two words' literal meanings are the same, and it's only modern usage that distinguishes them, as sibling comments argue.