The AskHistorians Wiki Calendar section has a fairly extensive catalogue of date/calendar origins that you may find your answer in if none present here.

can you also address month-day versus day-month differing origins.

Since I made a joke answer to your question the other day, I feel I need to respond more seriously now :)

This answer by /u/Enrico_Dandolo to an earlier question should be exactly what you're looking for. Also read the other responses there for some more in-depth material.

If you're looking for more information, do check the out the FAQ/Wiki (linked in another response in this thread).