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.
Although ‘resilience’ is more commonly used, ‘resiliency’ is not incorrect. Both terms have been in use for approximately five centuries. It was only in the late 19th century that ‘resilience’ began to be used more frequently by a significant margin. However, there’s no compelling reason to avoid using the shorter and more common form, ‘resilience.’
The ngram below, which graphs the words’ use in a large number of American texts published from 1800 to 2019, 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:
