I think you're mixing up a couple stories there, but it doesn't really matter that much. Just to fill in the details (and because the alternative is for me to start responding to work emails which I just don't feel like doing this morning): Babbage was concerned about the quality of mathmatical table books, which were used for calculations before we had modern calculators and slide rules weren't mainstream. The figures in them were computed by hand, and some were so bad there was an error on every page, which made them useless for scientific work and dangerous for industrial work. The Difference Engine was designed to print out pages of figures using a little printer attachment.

ENIAC was ininitially put to work calculating artillery trajectories, once the programmers figured out the bug where the shell kept going after it hit the ground (oops!).