No - A doubled die originates from the die that was used to strike the coin. It is the die that possesses the design doubling characteristics which is duplicated on the coin when struck by the die but the coin is only struck once by the die. A double struck coin is a coin that has been struck by a die multiple times. A doubled die is attributed to an error in the manufacturing of the die. A double struck coin is attributed to an error in the manufacturing of the coin.
The original coin at the top of this thread was struck from false or fake dies. The '55 cent above is an example of what used to be called the "Poor Man's Doubled Die", because the last 5 looks doubled - - but was struck from a worn die.