Difference between to watch over and to see in Korean
지켜보다·보다

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.

보다to see
(보다) means to see, look at, or watch with your eyes. You use it when you notice something, look at a person or thing, or watch TV or a movie. In daily conversation, you will often hear forms like 봐요 or 봤어요.
The difference
보다 is the general word for seeing or watching. It does not usually mean staying nearby and paying attention for some time.