The difference is the sound of the knock on the door, versus the fact that a person is waiting when there is a knock at the door. A knock at the door can also be symbolic for opportunity....

the phrase knock on the door usually uses knock as a verb. knocking on a door is using the knuckles of the hand to hit a door to get the attention of someone on the other side of the door. while the other phrase uses knock as a noun. A knock at the door is the sound that someone hears when another person hits a door with their knuckles. it can also be interchangeable hope it helps:)

1. Knock at the door- Someone else is knocking. You are probably inside when and you hear it. You're not standing with the person waiting at the door. Someone is at your door asking to come in. 2. Knock on the door- the direct action of a person using their hand/fist etc to knock on the door to make the sound. You might be the one knocking on the door. 3. You'll hear Knock on the door as a command in directions often (but it can also be shortened to just knock) For example "Please knock on the door before entering" "Please knock before entering" both those are the same thing. 4. Sometimes you'll hear in real life "I heard a knock on the door" "I heard a knock at the door" "Was there a knock at/on the door?" "Who knocked on/at the door?" used interchangeably in that context. But if you follow number 1 and 2 ^^ above then you'll be right. I'm speaking American English.

There was a knock at the door. Knock on the door and see if they are home.