An envelope with its flap on the long edge is always known as a wallet or a banker.
This style of envelope is very common and can be used in all applications.
Although widely available with a straight flap, the mailing wallet envelope often has a trapezium shaped flap which is suitable for use on automatic mailing machines, and a banker envelope’s flap has a triangular shape which is traditionally used in the greeting card industry and for personal letter writing. These may also be referred to as Greeting Card or Invitation Envelopes.