If you were gazing at someone ,it would be because you might feel very attracted to them or be in love with them. If it were an object, it would be because you were full of admiration it or wished to own it - eg a Lamborghini in a car showroom. If you were staring at someone, it would be due to curiosity, shock, anger or aggression and is considered rude. In fact we say to children " Don't stare! It's rude"

Hi Saleh, That's a good question! I'd say gazing has more positive connotations than staring does. You gaze at something out of interest or because it makes you feel a sense of wonder, examples of this are gazing into someone's beautiful eyes or gazing at the starry sky. When you gaze at something then, you're often admiring it. You stare at something when you're focusing on it or alternatively, when you're being absent-minded. Examples of this could be staring at someone who is acting strange, or staring at a wall because you lost your train of thought. I hope that made some sense!