Will to Fight was Determination's original Common Spell Card, alongside Resurrection. Effect updates and description changes can be seen here.
Current Order: Toriel -> Alphys -> Undyne -> Sans -> Papyrus -> Asgore.
Since Beta 48.0, Will to Fight adds the next Lost Soul in the cycle, a 3G Dust monster, to the top of your deck with +2/+2 and Haste. This allows it to guarantee a trigger of its Dust most of the time by attacking something it would die to. But the HP boost makes it harder to do so.
Check the Lost Soul image for the order they are given. It matches with DT's Passive as well as Resurrection and Another Chance. Universal among all 'Lost Soul Generators', Thrashing Machine cannot be obtained. If any of the 3 spells is used by a non-DT player and they obtain a Lost Soul, it will instead be a random one.