Just Except that much of the pay gap stuff comes from the fact that women's opportunity to earn is less because they are the ones expected to take time off for childrearing responsibilities (including time off school for sickness over the years). (Very simplistic, but I cba to go into a lengthy thing)
In the public sector, men and women (as far as I am aware and understand) follow the same pay scales. A male teacher, for example, will earn the same as a female teacher at the starting point. The difference arises when a woman reduces her hours to part time because the family cannot manage with 2 full time workers, and it's just assumed that it will be she who goes part time and not the man. In most families, both partners choose to have the baby, not only the woman, yet it is the woman whose career is affected and whose pay is reduced.
I've never worked in the private sector, so I can't speak for that. But you're talking about it pay being equitable where people get paid the same for the same job. I am aware that, in the private sector, there is a fair amount of 'negotiation' that goes on for payrises etc. Men are more likely to negotiate for pay rises because it's seen as part of the desireable in business Type A personality stuff, whereas a woman will be less inclined to because they are brought up to be 'nice' and women are less well received when they are assertive.
I am aware my post does contain some generalisations, but the reasons they exist as generalisations is because that is generally what happens. We will all know of a man/woman who don't fit the model.
So it's equal opportunities/equality of access in that the barriers to achieving equality of outcome are removed.