A quick rundown on the difference from an article on Canadian health care:
The terms equity and equality are often used interchangeably, yet they represent quite different, if related, concepts. As defined by Webster's New World Dictionary (1988), equity is fairness; impartiality; justice; anything that is fair or equitable. Equality, on the other hand, is defined as the state or instance of being equal. This in turn is defined as having the same rights, privileges, ability, rank, etc., or of being the same quantity, size, number, value, degree, intensity, quality, etc.
To achieve equality in distributing a given resource, everyone would be provided with an identical amount of it. So, for example, if we were interested in dividing a pie equally, we would cut the pie such that every recipient would get exactly the same size of slice. Depending upon how important this was, we may be interested in ensuring that everyone got the same amount of filling, crust, topping, etc.
If, on the other hand, we were interested in cutting the pie such that we were aiming for equity in distribution, then things would become more complicated. We would need a richer understanding of what it means to be the most fair. And this understanding would depend on what we take to be relevant criteria for fairness.
"Equality" is bullshit in the context of oppression. Equality is "let's treat everyone equally regardless of circumstances", which means "let's treat marginalized groups as if they're part of the majority", which basically is code for "marginalized groups have to shut up or they're part of the problem". Marginalized groups do not have the same rights or privileges as their oppressors, and pretending that they do is straight-up oppression.
Equality is allowing straight allies to apply for scholarships earmarked for LGBTQ* students because everyone should have equal access to those funds - equity is recognizing that LGBTQ* youth are far more likely to be disenfranchised before and in college, and keeping that money ACTUALLY EARMARKED FOR THEM. Straight people, you start out with a much bigger piece of the pie already, stop fucking demanding that queer people let you have some of ours.
I don't fight for equality. I fight for equity. If you're an ally arguing for equality over equity, stop fucking calling yourself an ally.