The first patch was originally produced in 1960 to commemorate the general Apollo program that planned to someday put humanity on the Moon. The second patch was the official patch for the Apollo 11 mission in 1969 (each Apollo mission had its own patch). Patches were embroidered into various NASA gear (except spacesuits) prior to the launch of each mission and apparently, members of the Apollo 11 crew signed an Apollo 11 patch that was on the spaceship with them years later and gave it to the Mars 1 crew because “it seemed only appropriate that a patch, which witnessed mankind’s first giant leap, should be there for its second.”
Images courtesy of the Denault Space Program papers, MG 111. Apollo Program Mission Patches;The Making of the Apollo 11 Mission Patch.