Coronet Double Eagles were designed by James B. Longacre, and issued to accommodate the need for a large gold coin to facilitate large domestic and international transactions. Double Eagles were struck first in 1849 (Proofs only), with commercial minting commencing in 1850.
The Type 1 issue lacked the motto IN GOD WE TRUST. Type 2 Coronet Double Eagles included the motto IN GOD WE TRUST as directed by the Mint Act of March 3, 1865. Type 3 Coronet Double Eagles are William Barber's interpretation of Longacre's design. The most noticeable change is the denomination, which is now spelled out as "TWENTY DOLLARS".
While the Double Eagles of 1907 to 1933 are all generally referred to as "Saint-Gaudens" type, only the roman numeral dated High Relief issues of 1907 are purely of Augustus Saint-Gaudens's hand. The low relief, arabic dated issues of 1907 to 1933 are actually the work of Charles E. Barber, loosely copying Saint-Gaudens' High Relief design.
Upon the insistence of Congress the motto IN GOD WE TRUST was added to the lower reverse during 1908 in accordance with the Mint Act of March 3, 1865.
When coin buyers refer to "$20 Libs", they are generally referring to Type 3 Coronets; "$20 Saints" to 1908 and later With Motto $20 Saint-Gaudens.