For the old mechanical machines (whether powered by a crank or powered by an electric motor) yes, the term "adding machine" was because, for most, all they could do is add:

https://en.wikipedia.org/wiki/Adding_machine

"Subtraction was impossible, except by adding the complement of a number (for instance, subtract 2.50 by adding 9,997.50)."

A few fancier ones could multiply, but they would do so by repeating an addition some number of repetitions. Nearly all output their results on a paper tape much like "store receipts" today, only printed in ink instead of via thermal transfer paper.

You’re not wrong. They work very similar to binary arithmetic: basically the only operations they can do is increment, decrement, and shift left/right (but by 10)

But multiplication is just repeated addition, and division is just repeated subtraction. Some of the highest-end units could do square roots! Check out CuriousMarc’s videos.