Both the words, Expectation and Expectancy, have the same meaning 'The State/ Act Of Expecting' and 'Something Expected'. But the word 'Expectancy' occurs very rarely, and in most cases you'll see it as 'Life Expectancy', which means 'The average period that a person may expect to live' . Two examples for you: 1) Life expectancy is useful for insurance premium calculation. And 2) An indicator of expectancy (/ SOMETHING EXPECTED) in development.

An expectation is what you strongly believe will happen. Expectancy is the state of expecting something. It sounds a bit confusing, but I wouldn't worry about it too much. Expectancy is not a very common word, except for in the set phrase 'life expectancy'.