When the Torah was given, the mountain that God descended upon is referred to as הר סיני (Shemos 19:11/20). Elsewhere (33:6), what seems to be the same mountain is referred to as הר חורב, with “חורב” used a dozen times in the Torah to describe where the nation was when the Torah was given. Do the two names refer to the same exact location, or does each term refer to a specific (separate) area?
The Talmud (Shabbos 89b), as well as numerous other Midrashim (e.g. Shemos Rabbah 2:4), say that both are names for the same place, with “סיני” referencing us becoming hated for having accepted the Torah and “חורב” referencing the consequences for those who didn’t accept it. Several commentators say explicitly that סיני and חורב are one and the same, including Ibn Ezra (Shemos 17:9), Rabbeinu Bachye (Shemos 19:1), Chizkuni (Shemos 3:1), Rashbam (Devarim 28:69 – see Rashi there too) and Metzudas Tzion (Malachi 3:22).
Ramban (Devarim 1:6) says the two are not synonymous. Instead, חורב is the area near הר סיני, with the large desert that includes both חורב and הר סיני called מדבר סיני. [Interestingly, in the entire narrative of the giving of the Torah, חורב is never mentioned.] Nevertheless, despite his opinion that סיני and חורב are not the same, Ramban acknowledges that הר סיני is sometimes referred to as הר חורב (e.g. Shemos 33:6), i.e. the mountain that is in חורב.
The Vilna Gaon (Devarim 1:6) also says that חורב is not סיני, but differentiates between הר חורב and הר סיני as well. הר סיני is where the Torah was given, while הר חורב is where the nation was camped, and where the Mishkan stood. He adds (based on Chagiga 6a) that the general principles of the Torah were given at סיני while the details were given in the Mishkan (and therefore in חורב), which explains all the references to the mitzvos being given in חורב.
Rokayach (Shemos 19:17), based on the Mechilta saying that הר סיני was uprooted from its original location and placed over the nation, says that הר סיני was placed on top of הר חורב, “as if there was a mountain on top of a mountain,” with the nation camped on הר חורב and Moshe by הר סיני. No matter how we understand this Rokayach, the two terms must be referring to different mountains.
Despite these seemingly different approaches, we can synthesize Ramban with the Midrashim, with חורב referring to the area, and the mountain in that area referred to by both names. We can even add some elements of the Vilna Gaon, with the Mishkan being in חורב, next to הר סיני, and the nation camped there (in חורב) as well.
__________________________
In his entry for רפידים in “Eileh Mas’ay” (Published in 5760), Rav Dan Schwartz says he is following Ramban’s opinion that הר חורב is not הר סיני (even though Ramban himself says that הר סיני is sometimes referred to as הר חורב; for our purposes חורב being separate will suffice for the point he tries to make). Because Moshe went to חורב for water while the nation was in רפידים (Shemos 17:6), R’ Schwartz says חורב and רפידים must be near each other, with רפידים to the west of חורב, and הר סיני east of הר חורב. However, Rashi (Shemos 19:2, based on the Mechilta), says that the nation camped on the east side of הר סיני. If רפידים was west of הר סיני, in order to get from רפידים to the east side of הר סיני the nation would have pass הר סיני, going around it, which seems awkward. [This would be true even if הר סיני and הר חורב were one and the same.]
Because of this awkwardness, Chizkuni asks how the nation could have passed הר סיני before the Torah was given. His question is based on the assumption that the nation traveled east from Egypt towards הר סיני and then further east on their way to ארץ ישראל (and not just from רפידים to הר סיני); bear in mind that Chizkuni is of the opinion that the nation didn’t cross the Yam Suf, but exited on the same side they entered, traveling parallel to its northern shore from west to east. R’ Schwartz (elsewhere) assumes that הר סיני is on the southern part of the Sinai Peninsula, which means they didn’t only travel east, but south as well. [I know, I haven’t really discussed the location of הר סיני here yet. But they were camped there for the rest of Sefer Shemos and all of Sefer Vayikra, so there’s still plenty of time; stay tuned!] Since they traveled both south and east, רפידים might have been north (or northwest) of חורב, and getting to the east side of הר סיני may not have required going around it. [I will add that if there wasn’t enough flat terrain on the other sides of הר סיני for the nation to camp there, going around it to get to the east side shouldn’t be an issue.]
Based on our synthesis of Ramban and the Midrashim, with חורב being the area and הר סיני a mountain within חורב, the relative location of רפידים in regards to הר סיני is less of an issue. Since חורב surrounds הר סיני on all sides, and רפידים could be north (or northwest) of it, Moshe could have gone south to hit the rock in the northern part of חורב, allowing the water to flow north (or northwest) to רפידים, while the nation subsequently traveled south (or southeast) to the eastern part of חורב, just east of הר סיני, without having to go around it.
Rabbi Dov Kramer wrote about the location of Har Sinai in 5776; it can be accessed at https://rabbidmk.wordpress.com/2016/08/04/parashas-matos-masay-5776/. He hopes to revisit the issue in these pages in a few weeks.