Sotah, Chapter 8, Mishnah 7. This Mishnah concludes the discussion of going out to war, and in it the Mishnah qualifies all the laws taught in the earlier Mishnayos of the chapter.
The text of the Mishnah:
"Bameh devarim amurim - b'milchemes hareshus, aval b'milchemes mitzvah hakol yotz'in, afilu chasan mechadro v'chalah michupasah" - When do these words apply? To an optional war, but in a war that is a mitzvah everyone goes out, even a groom from his chamber and a bride from her wedding canopy.
Everything stated above - that one who has begun something new in his life need not continue in the war, that some are not required to fight but only to serve in the supply system, and that some do not go out at all - was said specifically with regard to an optional war. But in a war that is a mitzvah everyone goes out, and it makes no difference if the groom and bride are in the very days of their wedding.
The words of Rabbi Yehudah:
Rabbi Yehudah uses very similar language, with a change in terminology: "Bameh devarim amurim - b'milchemes mitzvah, aval b'milchemes chovah hakol yotz'in, afilu chasan mechadro v'chalah michupasah" - When do these words apply? To a war that is a mitzvah, but in an obligatory war everyone goes out, even a groom from his chamber and a bride from her wedding canopy. The war in which there is a possibility of being exempted from going out based on a person's circumstances is called by Rabbi Yehudah "milchemes mitzvah" and not "milchemes reshus," while the war in which everyone goes out he calls "milchemes chovah."
The Gemara's explanation:
The Gemara clarifies that the word "reshus" in the language of the Sages and the word "mitzvah" in the language of Rabbi Yehudah refer to one and the same type of war. Both agree that in those wars there is a possibility of not going out, and both agree that in the war which the Sages call "mitzvah" and Rabbi Yehudah calls "chovah," everyone is obligated to go out.
Three types of wars:
The wars of Yehoshua - wars fought in order to conquer Eretz Yisrael. Everyone agrees that these are an obligatory war.
The wars of David HaMelech - which were intended only to expand the borders of Eretz Yisrael. These are certainly an optional war.
The middle category - a war in which there is no aggressor currently standing against Israel, but rather a preventive war: to make sure that the nations and enemies will not come against Eretz Yisrael. Even though they are not coming to fight now, Israel goes out against them in order to prevent what might happen in the future.
The dispute between the Sages and Rabbi Yehudah concerns precisely this middle category: Rabbi Yehudah calls such a war "milchemes mitzvah," and in his view the possibility explained in the earlier part of the chapter applies to it, so that one who has just married a wife and the like need not go out; the Sages call it "milchemes reshus."
The root of the difference in terminology:
Why do the two use different terms? The matter is connected to the principle that one who is engaged in a mitzvah is exempt from another mitzvah. Rabbi Yehudah relates to this type of war - the middle category - as a war that is a mitzvah, and therefore one engaged in it is exempt from performing another mitzvah. The Sages hold that this middle war is also called an optional war, and therefore it does not have the power to exempt a person from performing ordinary mitzvos on account of his involvement in the war.
In summary: In this Mishnah we learned that all the laws exempting a person from going out to war were stated only with regard to an optional war, whereas in a war that is a mitzvah (in Rabbi Yehudah's terminology, an obligatory war) everyone goes out, even a groom from his chamber and a bride from her wedding canopy. We examined the three types of wars - the wars of Yehoshua to conquer the Land, the wars of David to expand it, and the preventive war that lies between them - and saw that the dispute between the Sages and Rabbi Yehudah focuses on the middle category, with its practical difference regarding the principle that one who is engaged in a mitzvah is exempt from another mitzvah.