Rav Nechemia Raanan offers a different formulation in explaining Haosek Bemitzva Patur Min Hamitzva.
Ones vs. Ptur
- Ones- can’t physically do both mitzvas at once. Therefore the Torah says to continue the current one uninterrupted.
- Ptur- when engaged in service of Hashem, new mitzvah obligations don’t ‘catch’ and therefore you aren’t obligated in them at all
At first I suspected that he was just stating the same chakira that Boaz Kalush did with slightly different language, but after some thought, I would argue that his formulation is not an equivalent one.
Even though Rav Raanan also brings the nafka mina of Tfilat Tashlumin, he doesn’t mention the last three nafka minot(labeled 2A, 2B, and 2C in the previous post) and, in fact, they shouldn’t apply according to his svara. Those aren't cases of Ones vs. Ptur, rather they are clearly cases that deal with the question of different levels of ptur(especially the two dealing with מצוה עשה שהזמן גרמא). So while Rav Raanan questions whether Haosek Bemitzva Patur Min Hamitzva is truly a Ptur or rather a special case of Ones, Boaz’s takes for granted that we’re talking about a Ptur and focuses on the question of severity.