What is the difference between a cross-training shoe and a running shoe?

I just bought the Womens NIKE without limits and it is a training shoe. I already have a running shoe (from Saucony) that I use. My new shoes, however, look a lot like running shoes. What’s the difference?

How do you decide on the best cross training shoe for women?

I am looking for a real cross training shoe, not a running shoe. Is there somewhere womens sport shoes are rated for quality anf price?