I don’t know that I’d go so far as to call it different “kinds” of miasma, but it’s certainly different once you get into the details of it. For instance, say I spend a day outside, hard at work in my garden. The result is that I end up covered in dirt, so if I asked you to describe my state, you’d probably say, “You’re dirty.” True enough. But now let’s say I spend my day hunting, eventually killing a deer with an arrow to the heart. I field dress the deer and proceed to butcher the meat. This leaves me covered in blood and viscera. Then I ask you again, describe my state. And again, you’d probably say, “You’re dirty,” and again you’d be correct.
But then I ask you to go into detail. How am I dirty, in each case? The dirt from my garden and the blood from my kill aren’t the same sort of dirtiness, even though either way, I’m still dirty.
What I meant by my comment was that either way, I’m dirty. I’m miasmic. But if I present myself to Demeter in that field, covered in the dirt of my garden, I’m personally of the opinion that She’d be more willing to forgive it than if I presented myself to Hera in such a state. Or if I presented myself to Artemis covered in the gore of my kill, She’d be more likely to see it as an act that honors her as opposed to if I showed myself to Hermes that way.
It’s all miasma, but I’m personally of the opinion that the source of the miasma is important to understanding why the gods may not want it around them. Miasma is something that separates us from the Theoi; it’s the unshakable humanity we have that, as deities, they do not. Things they find distasteful or offensive about our humanity. Try to imagine being an immortal being and something comes to you, covered in death. A heaping pile of no thanks, right? But one of the things I love most about the Theoi is that They rule over these very human experiences, too. Artemis rules over the hunt, which inherently involves death by its very definition. Ares rules over battlefields, which are always covered in death, too. Demeter rules over the harvest which is dirty, sweaty work. And on and on it goes, because we are humanity and They are our gods. So I believe that They’ve got a bit of a…tolerance, if you will, for Their own areas of expertise. That’s why I think the source of miasma matters.