Quelle est la différence entre futur proche et futur simple?

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Futur proche = close future, about to happen
Futur simple = normal future, don't know when it happens

Futur proche
Je vais manger. = I'm going to eat.
= it's going to happen very soon

Futur simple
Je mangerai. = I'll eat.
= we don't know when

Futur proche is used quite a lot in daily conversation to talk about something you're going to do from now or at some time in the future. (decided).
That being said, futur simple can mean the same if it's used with temporal factors.

Je vais t'appeler demain.
Je t'appellerai demain.
= exactly the same, "I'll call you tomorrow."

Je vais t'appeler. = I'm about to call you. / I'm going to call you.
Je t'appellerai. = I'll call you. (we don't know when)