Does getting mad mean the same thing as getting upset? Is there any difference at all?
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In the US at least, being "upset" is not quite the same as being "mad". To be upset is to be mentally unsettled, moved out of your mental or emotional comfort zone by something. The resulting emotions from the upsetting stimulus could be sadness, frustration, hysteria, and/or anger.
By contrast, being "mad" implies one singular emotion, anger. "Mad" is synonymous with "angry"; though the term "mad" originally meant "crazy" or "insane" in American English, and in the UK it still does, but it is commonly used in the phrase "mad with rage", which was shortened back to "mad" in its current AE meaning.
The adjectives mad and upset are slightly different. Mad means:
enraged; greatly provoked or irritated; angry.
While upset means:
to disturb mentally or emotionally; perturb
You would get mad if somebody did something to make you angry, but you would get upset when someone did something to perturb you mentally. They are very slightly different, because mad and upset are different reactions to events that may happen.
"Getting mad" is more common in the US than the UK but in common usage their meaning is roughly the same. That's not to say "mad" and "upset" are the same thing.
The main difference between "getting mad" and "getting upset" is that "upset" could be just very sad and tearful, whereas "mad" implies acting irrationally, usually through anger rather than sadness.