Right. So you're saying an employer will advertise a job with a different rate of pay depending on whether the applicant is male or female. Can't say I've witnessed this.

I'm saying that in the Western world, anyone who completes their education, leaves school and gets a career which they work hard at for 20 years will be earning the same salary regardless of their race or gender.

Compelling argument.

From your description, I could only guess the reason this discrimination exists is because women in positions such as yours aren't aware of their rights and are not pursuing legal action when their rights have been violated. In your case, where you claim to have found evidence, I certainly hope you sought legal advice to help prevent this from happening to others.

Is this a 10-20% gap in specific jobs where males and females are equally educated, have equal experience and working equal hours, or is this gap just a general statistic about average male wages vs average female wages?

I'm not going to deny that discrimination exists. Of course it does and it always will, but laws are in place to prevent that. If those laws aren't doing what they're meant to do, we need to assess why. You say it's very difficult to prove and I believe you're right about that, so it would seem the problem lies with the courts and the methods with which the laws are enforced. It also indicates that perhaps people need to be more aware of what their rights are and when they are being violated.