Both mean ‘to forget’.
잊다 is the standard word you will probably learn for ‘forget’. It’s a more formal term; you can use it in informal, casual conversation or in a formal setting where you’re giving a speech or talking to someone you don’t know.
This word is more casual. You can use it in informal and casual settings and conversations, but you should definitely not use it in formal settings or with people you don’t know well.