Essentially, the difference between the two sources you cited is the difference between Mishnah and Talmud (in their original senses, as in Sotah 22a, Kiddushin 30a, Bava Metzia 33a-b, etc.). "Mishnah" is the basic halachos; "Talmud" is the analysis of those halachos, including also the application of them to different scenarios and conditions. (The Rambam, Hilchos Talmud Torah 1:11-12, calls the first one "Torah shebaal peh" and the second one "Talmud.")
So the "Mishnah" part, the actual halachos, continued to be said כנתינתן מסיני; everyone knew them clearly. The "Talmud" part is, as you said, subject to human variability, and that's where they would need to resort to the Sanhedrin (as indeed implied in Devarim 17:8ff, כי יפלא ממך דבר למשפט).
Over time, of course, things migrate from "Talmud" to "Mishnah," in the sense that once a halachah is applied (via "Talmud" analysis and, if necessary, a vote of the Sanhedrin) to a certain scenario, then that becomes "Mishnah," settled case law. (For example, the Baal Hatanya writes in his Hilchos Talmud Torah 2:1 that the Tur, Shulchan Aruch and Rema - where many of the halachos come from the Talmud - are categorized as "Mishnah" for purposes of Torah study, while the commentaries on them count as "Talmud.")
The Rambam, in his introduction to Perush Hamishnayos, draws such a distinction within the "Mishnah," between the halachos that were known to have been given to Moshe at Sinai (which remained clear and were never subject to debate, even after machlokes began to proliferate) and the halachos derived later on (such as via the 13 Middos), where there was unclarity, and thus dispute.
In short, then, the Gemara in Sanhedrin (should be 88b, by the way) is talking about "Talmud" and the halachos derived from it; Rashi is talking about "Mishnah," where originally both parts of it were clear, and later on only one part of it - the ones known to be Halachah Lemoshe Misinai - remained so.
To give an example, using the first Mishnah of Berachos:
מאימתי קורין את שמע בערבית: that Shema has to be recited in the evening (ובשכבך), and that there exists a definition of when this begins - universally accepted, and never lost. Every talmid chacham, from Moshe down to our times, learned this כנתינתו מסיני (not necessarily with the same wording, of course; Biblical Hebrew would probably have been מן מתי or something like that.)
משעה שהכהנים נכנסים לאכול בתרומתן: includes two points: (a) that kohanim who were tamei (and toveled) have to wait until "evening" to eat terumah, and (b) that this is the same time when "evening" begins as far as Shema. (a) is also universally accepted (based on the known facts that ובא השמש וטהר means טהר יומא, and that ואחר יאכל מן הקדשים refers to terumah), while (b) is not (as we see that the Gemara there brings several other opinions). In other words, at one time all talmidei chachamim knew and learned when "evening" begins for both of these purposes; later on they still knew and learned (a) כנתינתו מסיני, but weren't sure about (b), and so argued about it.
עד סוף האשמורה הראשונה... עד חצות... עד שיעלה עמוד השחר: obviously a matter of machlokes. From Moshe until the Zugos, it was known (it may have been decided by a vote of the Sanhedrin, for example) that ובשכבך delineates a certain time of the night, beginning at time X and ending at time Y. (It's also possible that in one generation the Sanhedrin voted one way, and in a later generation differently; see Rambam, Hilchos Mamrim 2:1.) But later on this was forgotten, and so different Chachamim try to reconstruct X and Y, each in their own way.
