Is a shot that hits the woodwork considered a shot on target? Apparently this is not counted in the EPL and La Liga? Is this true? I searched all of this extensively but could not find anything.
It depends on who is taking the records.
The argument for excluding it is that being on target means it should go in unless it is blocked. It wasn't blocked and didn't go in, therefore it's not on target.
The argument for including it is that being on target means it would hit the face of the goal, which includes the face of the posts and crossbar, so hitting these is still hitting the target and therefore it was on target.
No, a shot on target is anything inside the woodwork.
If a shot was inside the woodwork but deflected onto the woodwork then this would count as a shot on target.