The hills we choose to die on - Battle of California

For the NHL, term limits on contracts are "the hill they will die on", meaning that negotiating on that topic is futile -- they will not budge. But they're not the only ones who have that kind of topical stubbornness

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The Boston Massacre: An Interactive History Adventure (You Choose: History): 9781429620123: Raum, Elizabeth

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Does the phrase 'is this the hill you want to die on' mean the same thing as the phrase 'choose your battles'? If not, how do they differ, both in meaning and