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I understand the approachs to cut off and dimensional regularization and how these can be used to remove divergences in a theory when it is interpolated from the small scale to the large observable scale.

I also understand how renormalization groups can be used to find beta functions and scale invariance of a theory. However, in finding these beta functions I have been deriving and finding the Wetterich equation using functional derivatives of the partition function etc. and I am not sure how this links in to regularization and renormalization that I have previously been studying. I know that in RG equations the cut off is introduced in the regulator, when finding effective average actions, but this doesn't seem anything like regularization?

Can anyone please clear this up for me please, as I know they must be linked somehow

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