I applaud you for taking on this question and getting into the details. I wish you would had included links to the studies you were talking about so I could respond to the exact figures you were looking at.
Here’s what I got from the AAUW. It says the median annual wage of women working full time is 80% of the annual wage of men working full time.
The study declares women are concentrated in lower paying jobs and make less within many broad job classifications. For example female lawyers have median income that is near 80% of median income for male lawyers. What is unexplained is whether a statistical model with a finer breakout and more independent variables including number of years practicing law, law school, type of law practiced, and hours billed could not explain salary differences well enough that the gender variable would add nothing of statistical significance. Until we see the magnitude of the coefficient for gender, tests of statistical significance on the coefficients, and the explained variance (R^2) of alternative models, the case for gender as a necessary explanatory variable is suggestive at best.
The key point is that the use of amateur statistics to make a conclusion about gender wage discrimination is needlessly indirect. If such discrimination exists, why doesn’t the study directly cite a dozen examples where women were getting lower pay for equal work? Why doesn’t it have a list of companies in which people with the same qualifications and experience who work the same hours get paid different salaries? The answer is simple. Actual wage discrimination is already illegal and has been for 50 years. If you had a case of such wage disparity, lawyers would be all over it. Do a search of employment lawyers and you will find no want of attorneys eager to pursue a discrimination lawsuit. Big corporations have HR departments that push internal affirmative action in hiring and promotion to ensure no apparent violation occurs in their company. By and large they have been successful.
Women probably would have higher wages if they took more STEM courses, if they were more highly represented as electricians, plumbers, and in other trades, if they worked more hours, if they moved to occupations with less vacation, or if they switched to more lucrative professions. Those factors and others likely explain any nominal wage disparity. We thus conclude the statistical case for gender discrimination is fairly weak, at least with the data provided and the modeling cited.