I dunno. Crazy=angry in the U.S. tends to appear only in a couple of idioms (“he went crazy”). I don’t ever recall observing someone pointing to a person who was really upset and remarking “He’s crazy” unless the angered person was really ranting and raving and throwing himself about as if he was insane.
“He’s mad,” however, can be used in any context from complete rage to mere sullen displeasure.
On re-reading Casdave’s post, I guess we’re not that far apart. I initially read “enraged” as “really angry,” but it certainly carries a violent connotation.
"The original sense of the word mad is ‘mentally disturbed; insane; deranged; crazy’, a sense still in popular use (though no longer in medical use). The word, common to other Germanic languages, is found in English about a long as there has been an English in which to find it.
"While mad meaning ‘angry’ hasn’t been in English quite this long, it is still very well documented: first found before 1300, it was used in Shakespeare and the King James Bible, Trollope, William James, Yeats, Flannery O’Connor, and John Steinbeck.
"Despite this, people have been objecting to this sense since the late eighteenth century, with varying degrees of hostility: sometimes it is called “colloquial,” sometimes a “vulgarism,” sometimes “careless,” sometimes “informal,” and sometimes “slang.” In recent American usage, though, hardly anyone objects to the word; it is standard. Most dictionaries don’t give it any label–even the generally conservative American Heritage Dictionary, in its third edition, leaves it unlabelled, though the second edition had called it “informal.” Contemporary usage books usually ignore it as not even requiring mention, some simply call it “informal.”
"In British English, mad meaning ‘angry’ is still informal and is something of a usage issue (and is often considered an Americanism, natch). "