3 of 3 As Kris correctly pointed out, I forgot to insert what each actually means heheh so I've done that now.

Okay before getting all technical on the topic, let's try to figure out what do the two expressions seem to convey:

She came home angry expresses the subject's emotional state, without saying anything about its affect on the action of coming home. There is perhaps a weak cause-effect association, where her being angry may have caused her to come home. However this phrase says nothing (one way or another) about whether her being angry affected the act of coming home as she was in the state of that action.

She came home angrily again expresses the subject's emotional state, but it ties the state of being angry tightly with the action of coming whilst she's in the process of doing that action.

Whatever her mode of coming home (e.g. walking, running, driving or whatever) one can almost imagine her manifesting that anger into the action of coming. For example it conjures up the image of her driving rashly or bursting the door open when she comes in. There is an expectation of outward observable channeling of that anger in the main action of coming home.

I hope that you can see the difference between the two expressions at a level of conveying meaning.

Technically speaking:

In she came home angry the word angry is an predicate-adjective-clause that describes the direct subject namely She.

Whereas in She came home angrily, the word angrily is the attributive-adverb clause that attaches to the the phrase came home.

If you want to kind of visualize it, the associations are something like:

(she came home)(angry)

and

(she)(came home angrily)

If we were to use modern predicate grammar, the former would be:

came(angry(she), home))

Whereas the later would be expressed as:

angrily(came(she, home))

P.S.: I noticed earlier that, if spoken left to right, ignoring parentheses, it seemed that predicate grammar expressions sounded like Yoda speaking. It still seems so.