What is the difference between an associates in science degree and an associates in applied science degree in nursing?

An Associates in Science degree is a more general education degree, including more humanities and general sciences. An Associate in Applied Science, nursing or otherwise, is a more targeted degree for that profession. A "regular" associates degree is more transferrable to a Bachelor's degree and more all-purpose (can be applied to several jobs but in a general way), whereas an "applied" degree is more likely to get you a specific job (but no other job).