Problem: Exodus 19:11 affirms that Moses received the Law at “Mt. Sinai” (cf. v. 18). But here in Deuteronomy 4:10 it claims that Moses got it “in Horeb.” Which was it?
Solution: There are several possible explanations of this discrepancy. Some scholars believe Sinai may be the older and Horeb the later name for the same place. Others hold that Horeb may be the general name of the mountain range and Sinai the particular peak. Still others believe Sinai is the name of the entire group of mountains, while Horeb refers to one specific mountain. Or, the two names could be interchangeable.
In any event, the biblical authors, many centuries closer to the original event than we are, saw no problem in using both names. Horeb is used 17 times and Mt. Sinai 21 times in the OT. Employing two different names is not uncommon. Mt. McKinley in Alaska, the official name of the highest peak in North America, is called Denali by native Americans and many others.