No, it's not the same thing as a 1955D Lincoln cent. Instead, a 1955 doubled die Lincoln cent is one that was struck by the US mint with a major error in the striking process. These coins are worth a bundle today: thousands of US dollars for a nice example like the one in the picture (see values below). A 1955D cent, minted in Denver and thus carrying a small letter D as a mint mark, is worth about $0.10 according to the catalogs - essentially the face value of one cent.
If you have a true 1955 doubled die Lincoln cent, there are several steps you should take to establish and preserve its value. These steps include authentication, grading, and encapsulation. We recommend PCGS, NGC, ANACS, or ICG for this. Look these up on the Internet. Do not use other services.
Coin presses used by the mint rely on two important parts, called dies, to slam coins out of a pieces of raw metal. The pieces of raw metal are called planchets, and the dies strike the planchets with such force that the images imprinted in the dies transfer directly to the planchets, forming the coins. Sometimes the dies bounce a little as they strike a planchet. This results in minor imperfections in the coin called 'machine doubling' or 'strike doubling.' Coin collectors are not interested in this type of doubling, so such coins carry no premium value for collectors.
However, something that is valuable to coin collectors is a doubled die. What happens with a doubled die is that the mint makes an error when they are making the dies, not when they are making the coins. Errors on the dies show up as errors on the coins. This can happen when the 'master die' is used to create a die. Coins are almost never made from just a single die over a year, as the dies wear our after some many thousand or million strikes and must be replaced.