The Julian Date (Julian Day, JD) is the number of days since a chosen fixed time, specifically Noon, UT, November 24, 4714 BC Gregorian Calendar, (Noon January 1, 4713 BC Julian Calendar). Variants:
MHJD can mean "Modified HJD" as above, or can be used for a version adjusted by some other constant. Analogously for MBJD.
A Julian Year is somewhat distinct from Julian dates and the Julian calendar: it is exactly 365.25 days if 86400 SI seconds. It is used in astronomy as a measure of time.