This has been troubling me as of late. I know red and white are templars, white and black are knights hospitaller, and white and green are order of St lazarus, but I haven't found any information on these mysterious crusaders and I'd really like to know.
A white tunic with a red cross was the uniform of a Templar knight, but a black tunic with a red cross was worn by Templar sergeants:
- The surcoats of the sergeant brothers should be completely black, with a red cross on the front and back. And they may have either black or brown mantles; and they may have everything that the knight brothers have except the horses' equipment, the tent and the cauldron...And they may have a sleeveless coat of mail, hose without feet, and a chapeau de fer...
(Judith Mary Upton-Ward, The Rule of the Templars (Boydell, 1997), pg. 54.)
The white mantle and a red cross of the knights actually not mentioned in the Templar Rule, but we know about it from other descriptions.
For more information, here's a previous post I answered about the uniforms of both the Templars and Hospitallers.