"In the Orthodox Study Bible and my book The Bible and Holy Fathers
for Orthodox, often times one of the daily readings (usually the
epistle) does not match with what I find online on the OCA or Goarch
websites. For instance, today I have Hebrews 10:1-18/Mark 8:30-34, but
on their sites the epistle is from 2 Thessalonians.
Does anyone know or understand what the differences are, or why these differences occured?"
This has to do whether the jurisdiction is on the Julian or the Gregorian calendar. The readings begin according to when Pascha occurs and thus should be the same for all. But then we begin reading from Luke after the so called Lucan jump which occurs after the feast of the Exaltation of the Cross (Sept 14/27) and in which there would be a 13 day difference depending on whether you are on the OC or the NC.
This should only affect the Gospel readings though. If the epistles are different perhaps a different lectionary is being used that I am not aware of.