Shalosh seudos does include all 3. See Torah Temima on the relevant possuk. The Gemora explains that by eating 3 seudos on Shabbos we are saved from 3 types of tzaar, namely the war of Gog and Magog, the fire of Gehinom and the birthpangs of Moshiach.
He says that Leil Shabbos we don’t really get schar because we are so hungry. Same for Shabbos day seuda. But SS, especially in the winter, is difficult and since we put ourselves through tzaar, Hashem saves us from tzaar.