In his review on Effective Field Theory, Georgi emphasizes
Within the general framework of the effective field theory idea, there are two rather different approaches, which I will call the Wilson approach, and the continuum effective field theory approach. It is the second of these that I will discuss in detail here. But I should start by explaining why I think that they are different. I will argue that the two take a very different approach to renormalization. In Wilson effective theory, the fundamental question is How does the full theory change as you integrate out high momentum modes and look at it at larger distances? [...] In what I call continuum effective field theory, the question is How do we modify the theory to allow the use of a mass independent scheme and still get the physics right?
A longer discussion of the two perspectives on EFTs was recently here. Unfortunately, I'm not able to understand what Georgi or Rivat are trying to say here.
What exactly is the difference be Wilsonian and continuum EFT? Any help of reference would be greatly appreciated.