To me, they are the same.

They are equivalent to the English word "outside" (as a preposition and an adverb)

[preposition]

* 学校就位于镇子的外面。

- The school is situated just outside the town.

* 我们在图书馆外边见面。

- Let's meet outside the library.

[adverb]

* 因为下雨了，我们不能在外面玩。

- Because it rained, we couldn't play outside.

* 别让她在外边雨中等著。

- Don't leave her waiting outside in the rain.

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Similarly, 里面 and 里边 both means inside.

But as far as I know, unlike 外边, 里边 is not commonly used (I don't know why).

So, 里面 is recommended.