Why does a pizza stone make my pizza dough bread-like?
Your aluminum pan is allowing moisture to escape from the bottom and the top, whereas the stone does not, so the stone will have more rise.  To use a stone, after much trial and error, I have to roll that dough out super thin, like 3-4 mm, prebake in the hot oven for 4-5 minutes, pull it out, add the toppings, then finish for another 6-7 minutes.

Also, different flours will bring a different gluten content, which are the sticky bonds that will allow you to roll it thinner without it contracting at every roll.  I use 1/2 semolina flour and 1/2 plain flour, I can roll it thinner that way.

Be not dismayed, a breadier crust can be fantastic, you can load more stuff on it.