Difference between to be careful and to watch over in Korean
주의하다·지켜보다

주의하다to be careful
주의하다 means to be careful or to pay attention so that nothing bad happens. You can use it for safety, rules, or small mistakes in daily life. People often say it when crossing the street, touching hot things, or listening to important instructions.

지켜보다to watch over
지켜보다 means to watch someone or something carefully for some time. You use it when you stay nearby and pay attention, often to protect, help, or see what happens. It is common for people, animals, and situations, as in watching over a child or watching a game.
The difference
주의하다 means to be careful about something or watch out for danger. It is about caution, not watching a person or situation over time.