What's the difference between "no men allowed" and "no men allowed" on the door of the ladies' room?

Of course there is a difference. The first one is: You know this is the ladies' room. No entry. The meaning of not allowing. The second type: you can say that you didn't know this was a ladies' room, and you can go in, which is what you didn't know. Relatively speaking, the second expression is not as strong as the first one.