A prefix, 나 means 'move out(or forward) from somewhere'. it emphasize direction of action, 'outward'. 나가다, 나+가다 나오다, 나+오다. 나다니다, 나+다니다. walk out 나돌다, 나+돌다, revolve from the outside, around

They are essentially the same but 가다 means go and 오다 means come. So the translations would be come in and go in. So it depends where the speaking is if they are asking the other person to go into a room that they are not or come into a room that they are in. I hope this helps :)