As near as I can tell from a brief look at the book the OP cites, "strict" self similarity means you see similarity no matter where you look -- Addison gives the Sierpinski triangle as an example of strict self similarity and a spiral as an example that's self similar only at the center of the spiral but nowhere else -- while "exact" means you see an exact copy of the fractal at each point of self similarity, as opposed to something that merely has the same general appearance, which Addison calls "statistical" self similarity. All this is explained in the first few pages of the book, where the terms appear in boldface. Nothing there, though, is given with any mathematical rigor; whether rigorous definitions are given later, I can't say. (I was looking on googlebooks, which limits what's shown.)