The gemara quotes tana d'bei rebbi yishmael that point out the discrepancy in language used to refer to the paroches - in the parsha of the kohein moshiach (vayikra 4:6) it refers to it as "paroches ha'kodesh", but in the next parsha of he'elem davar it refers to it simply as "paroches". The Meshech Chochma (without even referencing our gemara) gives a simple explanation. According to most opinions (117a) a chatas yachid cannot be brought on a bama gedola whereas a chatas tzibbur can. Therefore, a chatas yachid can only be brought when the aron ha'kodesh is present. Therefore, by the par kohein moshiach which is a chatas yachid and requires that aron ha'kodesh, we refer to the paroches as "ha'kodesh" indicating that an aron must be there. But, for a chatas tzibbur we don't require an aron so by the par he'elem davar we simply refer to the paroches as a paroches because the "kodesh" aspect isn't necessary. Rashi on the pasuk of paroches ha'kodesh also offers a simple explanation. The sprinkling can't be on any part of the paroches, it must be aimed at the "kodesh" point of the paroches opposite the badim of the aron. However, Rashi on the pasuk of par he'elem davar is apparently troubled by not using the term "kodesh" in that parsha since the assumption is that there also the sprinkling must be opposite the badim of the aron, so rashi quotes the tana d'bei rebbi yishmael -
The tana d'bei rebbi yishmael explains derech d'rush - when the kohein moshiach sins the kedusha/shechina remains in place. But, when the majority of the tzibbur sins, the kedusha leaves. It is a parable to a king who had most of his constituents rebel - אין פמליא שלו מתקיימת. Rashi explains that the king no longer can express his jurisdiction and control over the nation when they are rebelling against him.
The parable seems very strange. The halacha of par he'elem davar is not for the tzibbur rebelling against Hashem, it is brought as we learned in horiyos when the sanhedrin makes a mistake in p'sak and misleads the people. Why would this be reason for the kedusha to leave as if the Jews were rebelling against Hashem? I think that the peshat is that the aveira is not the cause of the kedusha to leave, rather the fact that most of the tzibur could be misled by sanhedrin and stumble in an issur kareis is evidence of the fact (a siman) that the shechina has left. The aveira of rov tzibbur isn't the cause for the shechina to leave, it is the effect. This is very meduyak in rashi - ואם רובה סרחה וכו' הרי הוא מסולק מחיבתם וכוק ואין לבו גס בהן כבראשונה, ה"נ כיון דרוב ציבור סרחה כביכול אין כאן שכינה. Rashi doesn't say that the shechina leaves when they do the aveira, instead rashi writes that if the aveira is done it is evidence that אין כאן שכינה.