Rendered pork fat vs lard vs bacon fat?

Not a lot, bacon is basically brined and smoked pork (the process/recipe depends on where you live)

Fat does not actually change in flavour as much as the flesh does when smoked

"Rendered fat" is just the fat that has run off when heating meat. It should be pure fat, with all the impurity left behind, or skimmed off

Depending on where you live, lard is either just pork fat, or a common word for animal fat

In Asian cooking if it specifies pork fat I would use that. Most Schezuan recipes are not smokey flavour based, so it may be noticeable, and appear unusual