While those factors are certainly in the mix, there are still plenty of situations in which men and women in the exact same jobs, working the exact same hours, experience a pay disparity — that is, the man is making more than the woman.
Take, for example, the new law in Iceland working to address such disparities: https://www.npr.org/sections/thetwo-way/2018/01/03/575403863/companies-in-iceland-now-required-to-demonstrate-they-pay-men-women-fairly
Or the massive lawsuit against Walmart, in which women demonstrated a) that they were paid less than men for the same jobs, and b) that they were held back from higher-paying jobs because of their gender: https://now.org/blog/walmart-and-sex-discrimination/
Or the internal research showing that Google pays its male employees more: https://www.nytimes.com/2017/09/08/technology/google-salaries-gender-disparity.html
These are not isolated examples.