Hey Kallia,
The simple answer is that there isn't really a difference - both mean outside and can be used interchangeably:
我早晨上學的時候,外面正在下雪
天氣很熱,不少人索性在外面過夜
這些流浪漢一年一年都在外面浪跡天涯
In all of these sentences, 外面 can be replaced with 外邊 without issue.
As mentioned below, 面 is slightly more formal than 邊, but in spoken language you can use either. It's really personal preference.
Laurence