gender equality and feminism overlap a lot. but they're not exactly the same thing, are they? some fringe groups that identify as feminist kind of want to see men opressed, not equal. and some people might not want to use the label "feminist" but they believe in and fight for gender equality all the same.
No, you’re confusing a lot of things.
Firstly, the major movement for gender equality started with feminism. First wave feminism was really the first time in history that women got together as a cohesive movement and pushed back against societal structures. (It was also the first time in history that women weren’t, like, burned at the stake for trying to do so.)
So, it’s not that they ‘overlap.’ The gender equality movement that we know today lit-er-ally started with feminism. They are honestly one and the same. The basest definition of a feminist is someone who believes in the equality of genders. That’s like the minimum requirement to be a feminist.
Now, deep into 3rd wave feminism, feminism is a much more loaded word. 3rd wave feminism is more intersectional and isn’t just fighting for the equality of genders, but it fighting for all of the intricacies that are tied into equality as a whole—race, sexuality, economic situation, etc. There are feminists who may not agree with all of the above, because they are not intersectional feminists. That’s unfortunate, and a pretty narrow and dated view of feminism, but those feminists exist. Which brings me to this—
Here’s a thing to keep in mind: not all feminists are the same, or have the same ideology. I’ll give you an example. There are several different types of Christianity: Catholic, Lutheran, Episcopal, Baptist, etc. In the same way, there are different kinds of feminists: today you’ll run into mostly 2nd wave and 3rd wave feminists, liberal, radical, and social feminists, just to name a few. All of these kinds of feminists approach feminism in a different way and from a different standpoint. Often times there are things that are not universal across all of these feminist ideologies, and what ends up happening is an ignorant person will say “oh look, this feminist said this so that must be representative of how all feminists think.” But that’s as ridiculous as saying “well, this Christian said this so that must be representative of how all Christians think” because, clearly, it’s not. If it were, these different groups within the whole wouldn’t need to exist.
As to your example of the ‘fringe groups who want men oppressed’, well, continuing with the Christianity example, those feminists are the Westboro Baptist Church of feminism. They take what feminism (or, to use our example, Christianity) has to say and completely misconstrue it to the extreme. None of the sane Christians/feminists actually like those people, nor do we want to associate ourselves with them. But, all we can do to combat their hatred is do the same thing we do for misogynists—continue to fight against their prejudice with a message of equality. Like has been said a million times and will likely be said a million more, feminism and the eradication of gender roles in society will benefit men just as it will women.