Thank you for the additional definitions but the only thing I was interested in was that both mean: "enter".
What I understood from my experience.
1. When a man standing outside my closed door and he is knocking the door I say to him: Войдите пожалуйста!
2. When a man standing outside my open door and he is watching me (asking for permission to enter) I say to him: Зайдите пожалуйста!