#She came home angry

Here angry is an predicate-adjective-clause that describes the direct subject namely "She".  

#She came home angrily

Angrily is the attributive-adverb clause that attaches to the the "came home".

If you want to kind of visualize it associations are:

(she came home)(angry)


(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))

Hope that clarifies.

P.S.: I just noticed that, if spoken left to right, ignoring parentheses, it seems that  predicate grammar expressions sound like Yoda.