What are the two classifications of computers that Charles Babbage is responsible for?

Answer 1

He is famous for his mechanical machines he designed, the Difference Engine and the Analytical Engine, though he did not actually fully build them. They were completed by others after he died. He is also credited with inventing other things. He invented the frame at the front of locomotives that help clear items from a rail line, which is called a pilot or a cow catcher. He also invented an ophthalmoscope, a device for examining the eye.

Answer 2

Imaginary and hypothetical, perhaps?

Babbage never actually built a computer, and modern computers are very different from Babbage's design (among other things, Babbage's "analytical engine" was mechanical, not electronic).