Not exactly, they can be used the same way in most occasions, but they're different. To leave means that you're going away from here. To exit means that you're inside something and go outside.
At least in Hebrew there's a huge difference, when the thing you're exiting or leaving is your home or your work: every day you יוצא out of them, with the intention of returning later. When you עוזב, it's for good... I think in English "leave" can be used in the day-to-day sense, too.