In Pinball repair, this is how I define these words.

hack = modifying a broken part to make the game work using any method necessary. It generally consists of bypassing any broken or faulty parts because you don't have the correct part on hand, or you are just lazy.

mod = any alteration to the existing design for better or worse, but generally done with the intention of improvement, like putting fuses on the BRs on SYS11 games that don't have them. Ground mods in some cases I think belong in the "repair" category, because they are so crucial to keeping a game running properly, they're a necessity.

repair = replacing the broken part with the correct part and doing so cleanly and correctly so that it will last as long as the game is around, or any type of work needed to keep something running properly or as originally intended.

In my experience, the majority of the mods I have done have yielded very positive results, but you do have to have an understanding as to why you are doing them.