I found this reference very helpful in building a solid base for learning the foundamentals of Homogenization methods and up to now, is the only reference that addresses the difference between Homogenization and Averaging methods.
I will put more references in this entry and will be happy if you share your links with me.
G.A. Pavliotis and A.M. Stuart, "Multiscale Methods: Averaging and Homogenization," Springer, 2008