>>> only that the wage gap is not caused by differences in pay between men and women doing similar work in similar roles.

That's pretty much what is common understanding of the wage gap. If you understand by "wage gap" that less paid positions paid less, it's meaningless. If you understand by it that women more often work in positions that pay less, then it's not a wage gap - it is a position gap or promotion gap or whatever else gap. So calling it "wage gap" is misleading, as the wage is not the variable that changes between men and women - the position on which they get the wage is.