What's the difference between "incarnation" and "embodiment"? I didn't get a clear distinction from Webster. Is it like "incarnation" is more about a state and "embodiment" is more about an action? Or is it like "incarnation" is more about a living being and "embodiment" is more about an idea or a notion?
Incarnation is all about the previous state and a transformation after its life. If you say "This dog must be a rabbit incarnate", you are saying that the dog has a lot of rabbit like qualities. This may be physical (like ears), or the fact that they like to hop around. This also implies that the animal/person lived another life. You would always be an incarnate of a living thing.
Embodiment is to embrace or display a trait. You may say "This dog is the embodiment of joy". You can embody a lot of things, unlike incarnation, these can be non-living things. While they can mean roughly the same thing, there is some nuances in usage as well as meaning.