Is a Stacastic Model a Statistical Model?

I like your transition from models that we think of more broadly into the statistical realm. I will tell you, even models in the statistical world are, i'm not exactly sure what gets counted in a statistical model. Even if there were no stacastic component to an intercept in a slope, i would still call that a statisticalmodel. So whether it's deterministic or stoccastic is less relevant than are we imposing a structure that we believe represents the data generating mechanism? Do we have a mathematical statement and a set of associated assumptions? That said, this is what i believe is an approximation the process that gave rise to my data.