运气 ＝ Luck , their usage are almost the same. For example: 运气好 ＝ good luck, 运气差 ＝ bad luck. 福 = blessing which is more like good( and only good) things happens in your life. And it is probably because you help many people or did a lot of good things in your previous life. For example: A man marries a nice wife. We say that the man has 福气. I think the major difference between 运气 and 福气 is that 运气 depends on chances , and 福气 is earned.