No, they work out different body parts. Push-ups work the chest/triceps and chin-ups work primarily back/biceps. Palms facing you which is what I think you mean by inside hands would work arms more than palms away which is more back.
As for replacing pull-ups with pull-ups, well then that's an advanced concept beyond my scope of knowledge...
I think we are spending more time trying to figure out what he is asking than answering the question.
If he is asking about what the difference is between a pullup and a chinup, the differences are slight. There is a small difference regarding which part of the lat you use and how mch bicep is used.
If he is asking about doing pushups and bringing your hands closer together, the exercise is similar and you are using slightly different parts of your pecs and triceps.
I don't know how someone can think that they can replace pullups with pushups.