Women are not treated as equals to men. Period. There are thousand of studies that prove that men think women are talking more than them when they talk half as much, that women are considered bitchy and bossy when they are in control and are being agressive just to name a few things.
Yes, there is a distinct difference in how women and men are addressed. When men are being "nasty," it is accepted as manly, as 'boys being boys'. When a women is heard saying something offensive, it is unladylike and disrespectful. Women have fought for the right to be seen as equals, yet this has clearly not been accomplished to its fullest extent.
There have always been double standards in the way that women are treated/addressed and the way that men are. Women are talked down to by men, and treated as a lesser and weaker person. And it isn't just men, there are women who treat other women this way as well.
As we have seen in this presidential campaign on multiple occasions, men seem to think that it is appropriate to address women using crass sexist stereotypes in an effort to demean them personally rather than engaging with the substance of their argument. There is certainly a double standard when it comes to addressing men and women in public; men are permitted to run women down simply because they are female and women could never do the same in return.