My cat has just been trained to be wary of outdoors - she knows its there but just knows it pleases me that she does'nt go there.
Shes never been a stray so could not feed herself to save her life , I know she would be a great mouser but because none get in the house theres none for her to kill.
A cat will always act differently if it has has been semi wild it has a different perspective on life.
My cat goes in the back garden , but knows its a treat and as its well fenced off I am pretty sure she will not jump the fence and run away , she gets watched anyway .