provided that，providing that有区别吗？可以相互替代吗

没区别，可替换。
provided 如果；假如；只要 If you say that something will happen provided or provided that something else happens, you mean that the first thing will happen only if the second thing also happens.
Provided they are fit I see no reason why they shouldn't go on playing for another four or five years. 只要他们身体强健，我看不出他们有什么理由不继续再打四五年比赛。
providing 如果；假如；只要 If you say that something will happen providing or providing that something else happens, you mean that the first thing will happen only if the second thing also happens.
I do believe in people being able to do what they want to do, providing they're not hurting someone else... 我真的认为人们只要不伤害别人，自己想做什么就可以做什么。