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I'm assuming you are really asking this question, so I will try to answer.
"Provided that" is similar to "as long as."
The two words combine to make an expression that means "Under this condition," or "If X is so," or "If X happens," so they form the first part of a conditional statement : If...then.
"Providing" has a greater range of meaning just like any gerund from a verb: "Thank you for providing the new analysis," "Providing the new analysis was not as easy as we thought," "Who will be providing the new analysis?" etc.
That's how I would explain the difference without looking it up--because you could do that if you wanted to.

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They mean the same thing. You might find this discussion useful:
https://forum.wordreference.com/threads/provided-that-vs-providing-that.3364652/

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As a normal verb, provided is the past tense, while providing is the present tense.

In this phrase "provided that X" / "providing X", they're honestly pretty interchangeable. "Provided that" maybe sounds a little more certain that the condition is going to happen but honestly both of them imply the condition is more likely than not to be true.