Resilience and resiliency are different forms of the same word. Both nouns refer to the ability to recover quickly from illness or misfortune. But in 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.
The ngram below, which graphs the words’ use in a large number of American texts published from 1800 to 2000, suggests that Americans use resiliency relatively often and have done so for a long time:
And this ngram shows the two forms’ occurrence in British texts from the same period: