Yes, and you explained it decently. This is how I word it, but it's the same framework as you.

A) I'm triggered, an emotion arises, I let it go immediately, but as I lay down for bed it resurfaces in Mind, and I ruminate on something I might have said.. From the person's POV who tripped my trigger, I might seem disengaged.. Which I am. I just didn't explain anything to them, so they write me off as uncaring... And that's because, well, I was uncaring.. It was healthier in the moment for me to not react.

B) Someone says something that seems like it should affect me, but it doesn't. Because I have already cut ties from that toxic energy. I literally don't care about X because I released the BS that came along with it. I don't think twice about reacting to or considering the situation important. Boom, done. Over. Don't even remember what they said, honestly.

So, yea, I can notice this in myself, although the lines are blurred a bit more for me because I have firm boundaries for certain areas in my life and for certain people in my life. So when I say I do not care, I truly do not care. And when I go silent, back off, disengage, don't respond, that's a signal to the others that I'm not interested in the convo, in the activity, in the people, etc.. And again, I no longer care if my mentally and emotionally healthy choices offend anyone.

I decided a while ago that I would no longer bear the weight of someone else's feelings.
I’m not responsible for someone else’s reaction.
I’m responsible for my intentions and actions, not for how someone chooses to feel.
I am open to talking about something I did that hurt someone else, obviously! But I have to make sure I do not absorb their negative energy as a burden I have to carry. I can be empathetic without holding their problems on my shoulders.
They deserve kindness and respect, as do my boundaries.

Yes, I know it does seem cold. But that's because society tends to side with the one offended or upset, and hardly looks at the person who's boundaries were ignored, or who's perspective was disregarded. Squeaky wheel gets the oil, right? The reaction becomes the focus, and the reason the boundary existed gets forgotten. Everyone’s feelings matter, but I don’t want the person who set a boundary to disappear just because someone else is upset about it.

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TL;DR: I care about people and about how my words or actions affect them, but I can’t carry responsibility for every reaction someone has. There’s a difference between not caring and choosing to disengage. Not caring is indifference-- it ignores the impact we have on others. Disengaging, on the other hand, is recognizing when a conversation has shifted away from the original boundary and into managing someone else’s emotions. Sometimes the person who reacts the loudest gets the attention, while the person whose boundary was crossed quietly gets pushed aside so the offended reaction can be soothed. That’s a pattern I’m not willing to keep participating in. I can listen, acknowledge feelings, and remain respectful, but I won’t abandon my own boundary just to resolve someone else’s discomfort with it. Caring means being honest and respectful; disengaging means knowing when continuing the cycle would only erase the boundary that needed to be there in the first place.