My cat is pooping on the floor...?

I have two cats, a girl who we got around March and a boy we got in May- er (the girl) is 5 and Peanut (the boy) is 6. Just recently I threw out the disposable litter boxes and replaced them so they are immaculate. After cleaning, I moved one box a few feet away to a better location. I put both cats in there (one at a time) to show them and make sure they knew it was still their trusty litterbox, just in a new locale. This morning there was poop on the carpet (closer to the litterbox that moved) and last week there was one nugget of poop right outside the litterbox (the one that did not move). Also this morning, there was a vomit, too and I dont know which cat it was from. I have heard he might be pooping on the floor because the litterbox moved, but I cant really move it back. What can I do that does not involve moving the litterbox?