I constantly hear people use the word "resiliency" (especially sports broadcasters and the like). I've always used "resilience" instead. Is there a preferred word to use in any given situation?
As far as I can gather they are exact synonyms.
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Resiliency is just a variant of resilience. Which one is used is a matter of style and personal preference. I would always use resilience because it's one syllable shorter than resiliency. Others may have different opinions. It doesn't matter because they are, as you suggest, exact synonyms, except for the pretentiousness of the longer word: resiliency. All verbosity is pretentious.
Resilience is the more accepted form in the USA.
[I]n today’s English, resilience is far more common than resiliency, especially outside the U.S. and Canada. In North American publications, resilience appears about four times as often as resiliency. Outside North America, resiliency appears only rarely.
Though resilience is more common, resiliency is not incorrect. Both words are around five centuries old, and it wasn’t until the late 19th century that resilience prevailed by a significant margin. Still, there’s no reason not to use the shorter, more common form. - Grammarist
Resiliency has become very popular with sports broadcasters when describing the emotional grit of a team in competition. It is part of an alarming trend for former athletes to try to appear professorial in their post career work in television. It falls into the category of wearing unneeded glasses, never referring to a ball or a team without the full reference to the sport (football instead of just ball, football team instead of just team etc.). I wish all of that would die a quick death but it has incredible resilience.