Pikuach Nefesh on Shabbos\ Parashat Korach
In Parshas Korach the Torah tells of how a plague began after B'nei Yisrael complained about the death of the followers of Korach. Moshe Rabbeinu, applying the secret he was taught by the malach ha'maves (Angel of Death) himself, told Aharon HaKohen to burn Ketores (incense) in a pan and to stand between that dead and alive, thus stopping the malach hamaves in his tracks and ending the plague.
The Netziv in Ha'amek Davar raises the point that in fact doing what Aharon did, to offer the Ketores outside of the Mishkan, was a Torah prohibition and was only permitted because of
Pikuach Nefesh, the Torah rule that saving a Jewish life takes precedence over all of the Mitzvos (aside from the cardinal three - murder, idol worship and idolatry).
The Netziv writes one specific novel Halacha. It is agreed that even a mere doubt of Pikuach Nefesh is enough to permit all prohibitions. In such a case though, writes the Netziv, if it won't cause harm to wait for clarification one should wait even if doing so might require him to violate a more severe transgression in the end. For instance, if now is Yom Tov and the danger is unclear, even if tonight will be Shabbos which is more severe than Yom Tov one ought to wait until clarification. This of course is only unless waiting might effect the functionality of the treatment to any degree.
An interesting question was posed to the Ra'avad (Rav Avraham ben Dovid, around year 4900) with regard to Pikuach Nefesh. The Halacha dictates that when a person with a life-threatening illness needs to eat, an animal may be slaughtered for his sake on Shabbos. What's the Halachah though if he also has available a non-Kosher piece of meat - is it better for him to eat the non-Kosher meat thus not transgressing the Shabbos, or should he transgress the Shabbos and slaughter the animal in order to refrain from eating non-kosher.
Varying approaches are offered by the Rishonim. The Ra'avad's response, according to the Nusach quoted by the Rosh in the 8th perek of Meseches Yoma, was that since we anyway need to be Mechallel Shabbos to cook etc. for the person in danger, it is considered as if Shabbos has already been pushed aside for this Choleh and therefore better to slaughter for him than to feed him non-Kosher. (See the Rosh for an additional point.)
The Maharam MiRotenberg (around 5000) compares Pikuach Nefesh on Shabbos to cooking on Yom Tov, saying that once the Torah permits Melachah on Shabbos for Pikuach Nefesh it is the very same as a weekday and therefore there is no reason for him to eat non-Kosher. His Talmid the Rosh writes that there is a concern that if we give the sick person non-Kosher meat he will be disgusted and not be so quick to eat it thus endangering himself further. Therefore it is better to violate Shabbos in order to give him Kosher meat.
Another interesting and very relevant issue related to this is the question if , in the event where it won't delay or hamper the necessary assistance, one should try performing the Melacha with a 'Shinui', meaning doing it in an irregular way, thus avoiding a Torah prohibition. In the instance of bris milah on Shabbos there's no preference for one to try using his left hand or the like (even if he could perform a good job doing so) to try avoiding a Melachah Mid'oraisah (Torah prohibition), so maybe with regard to Pikuach Nefesh we can say the same thing.
The Rishonim (Ramban and others in the beginning of the 19th perek of meseches Shabbos) are clear thet there is a difference between Milah and Pikuach Nefesh in such that Milah on Shabbos is perfectly permitted like a weekday whereas Pikuach Nefesh is only permitted based on necessity and therefore should be avoided with a Shinui if possible. The Rambam on the other hand, according to the explanation of the Maggid Mishnah, as well as Rabbeinu Yeshaya MiTriani (Piskei Rid Shabbos 130), are of the opinion that also with regard to Pikuach Nefesh one needn't try using a Shinui, just like by Milah. The Rid adds that for the same reasonong there is also no need to ask a non-Jew to do the Melachah instead. The Ramah in Shulchan Aruch (O.H. 328, 12) says that the custom is to use a Shinui or a non-Jew when possible but adds that if there's any worry that the non-Jew will not work at as quick of a pace the Jew should not hesitate to do it himself. [How this ruling, to prefer a Shinui or a non-Jew, concurs with the previous ruling about the non-Kosher meat on Shabbos is a point of analyzation but is not within the scope of this Dvar Halachah.]
Another place where we find a differentiation between Milah and Pikuach Nefesh can be found at the very end of Hilchos Milah in Shulchan Aruch Yoreh De'ah. According to the Vilna Gaon (5480-5558) in the Bi'ur HaGra (266, 25) when a Bris Milah is performed on Shabbos it is permitted for two people to share the job, i.e. one to perform the Milah and the other, the Priah. One needn't limit the chillul Shabbos to one person only. This concurs with the ruling of the Ramah there in Hilchos Milah. The Gra writes though that this ruling is based on the fact that Milah is different than Pikuach Nefesh. Otherwise, he implies, only the one who began the job would be allowed to finish.
One last issue is that it seems from the Rambam in the 2nd perek of Hilchos Shabbos that being that Shabbos is like weekday with regard to a person with a life threatening illness, therefore all of his needs may be performed even if saving his life doesn't actually necessitate each and every act. The Bi'ur Halachah though (simann 328) questions this very strongly and rules that only if something might be necessary to save his life may it be done on Shabbos with a Melachah Di'oraissah.