There is a huge difference between those two.
Feminism: The advocacy of women's rights on the grounds of political, social, and economic equality to men.
As you have noticed: The main idea of feminism is to make both genders equal. So it started by talking about women's issues and trying to cover them all, and it worked very well, because now women can talk freely about their sex life, their feelings, their opinions and their horrific rape stories and speak up and defend themselves about harrasment.
After this huge, great evolution and leap to the gender equality, something happened. The femiNAZI appeared.
Feminazi: The term is used pejoratively in popular culture to describe either feminists who are perceived as extreme or radical or women who are perceived to seek gender superiority over men.
Feminazis are racist women who are doing exactly the opposite of what men a long time ago used to do. They are trying to rule and be the better gender, and by doing that they are forgeting the most important rule of feminism, the only thing that feminism was based of: "GENDER EQUALITY".
Feminazis fight for trivial things, and they forget what is important about gender equality. Feminazis want to change very old terms so it would contain "Women" instead of men.
For example, the world 'snowman' gets on their nerevs. How dare they call it a snowman! It is a snowperson!!! They would all say.
Also they think that bras are a sign of oppression and submission to men, even though it was invented to support the breasts and make women more comfortable.
They think that women shouldn't shave their legs or wear makeup because doing so is a sign of submession to men's desires. They thing that if we try to look good to attract men then we are being submessive. Hint, they don't mind men trying to look good for them.
Hope I tried to change your point of view about feminists, because me, as a feminist, I try my best to debate and support equality between both genders, and I believe women in the middle east should speak up about their issues and for example their rape stories and report them, just as men should do so in the USA, that is sort of getting dominated by feminazis.
Have a nice, equal, peaceful day!