I see women's rights or the women's movement as broadly referring to all kinds of ideas about justice for women, and women's place in society, particularly when those ideas or discussions are coming from women, across political boundaries, cultures, and even time. That's very broad obviously, and happens across very disparate environments, so the concerns and interests will vary hugely. A woman in medieval Italy is not going to have the same problems, interests, or solutions as someone living in modern Idaho.
What unites these people is that they have experiences and needs related to their female bodies, like the realities of pregnancy or motherhood, or in relation to the society wide consequences of being a sexed species.
Feminism, to me, comes out of a much more specific time and place, to a large extent its concerns and interests are focused on the context of the 20th century, its vision of what society is comes out of that period, and so do the theoretical concepts it embraces. None of that is necessarily bad, we all deal with the time we actually live in. But I find what gets called feminism seems to be very wedded to certain ideas that I just don't think really stand up, and to me have a parochial quality - the focus on patriarchy as the cause of women's oppression, a tendency to see technological modification of the female body as the only road to what it considers liberation, an assumption that freedom is the highest value, a tendency to take for granted the 20th century employment model as inevitably normative, a tendency to see the female body and motherhood as a problem to be solved, a tendency to be dismissive of family structures that most women want to exist within, and find supportive.
I would be happy enough to say that feminism is something else, and can absolutely encompass someone like KJK, or Mary Harrington, or MMurphy, or strong conservative, even Tory, women. But it doesn't really seem like it is.