The "4-way flat plug." has been a standard colour code for at least 20 years on boat trailers, skidoo trailers, box trailers and most light duty trailer applications.
The 6-way connector is also known as a "Cole Hersey Plug" and is used on some horse trailers and construction type (flat bed) trailers.
CAR END/TRAILER END
The 7-way plug is also known as a "Bargman connector" used mainly on house trailers.
CAR END/TRAILER END
The 6 and 7 way connectors are required because these types of trailers usually exceed the 2800 lb. legal limit for brakes and they are usually equipped with "Electric Brakes." That accounts for the extra connections inside the plug. In the case of a house trailer, the connector is also equipped to charge the battery on the front of the trailer for the water pump and inside lights.