I've never heard anyone refer to "grandma-style" pizza, though truly, what my own Calabrese grandmother made was essentially a half-height version of the Sicilian square pan served at GNR Freddy's, so I at least buy it as "my grandma's-style."
As
The Pizza Professor,* I strongly disagree with the characteriziation of Chicago style thin crust as "flaky...almost pastry-like." Most of the classics (Vito's and Nick's, Aurelio's, etc.) employ the same dough for other menu items, where it clearly has a yeasty bread profile, with no butter or real flake. I don't think even the seeping grease and sauce brings any pastry-like character to these doughs, and I think Joe Aurelio (PBUH) would have kicked anyone's ass what-a called his pizza "pastry." This debate usually leads to the recognition that it's pretty hard to pigeonhole the widely varying exemplars of Chicago neighborhood thin crust into one style anyway.
*although I need considerable help finding good thin crust in the Oak Park area - any recent suggestions?