Would you show the difference between "stare" and "gaze"?

Would you show the difference among "stare" ,"gaze" and " eye"?
I can't see how and when they usually can be used in any situations.
I think we can use "gaze" in this situation.
ex) In the street , I happen to see a pin-up girl so I gaze at her.

we can use " stare"
ex) In this situation that Mom and son are walking down the street.
at the opposite , A disable person is almost passing by them.
Her son is staring at the disable. His mom told him "You shouldn't stare at people, It's bad manners."

To sum up, "gaze" could be used the situation that causes the curiosity. or surprise. On the other hand,
"stare" ..in the situation that causes the negative feeling" or "to be felt rude"
Now I can't realize the sense of them yet.

Please Help me out .