An event is a planned public or social occasion that occurs on a specific date and usually lasts a few hours to a few days. There is a fixed agenda for an event. A concert, an audition or a competition is an event.
A meet up is an informal meeting or gathering of people where they meet and discuss things. A meet up can occur once or can repeat on specific days. There is usually not a fixed agenda and people are not bound by strict schedules. Writers can meet every Saturday noon to hang out and write, judge and critique each other.
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