The difference between 'Women's History' and 'History of Women'
The distinction that historians who study women draw is instead between "women's (slash gender) history" and "history of women."
"Feminist history" is basically any history that is or has been claimed as feminist (see also: John W. Campbell's "Science fiction is what I say it is"). This is classically a history focused on women, but not necessarily. Works that focus on men as men instead of men as a substitute for "people" can be explicitly feminist--this is the case of a lot of scholarship on male accused witches in the early modern era, for example. Gender studies--history of masculinities, femininities, the idea of gender, queer studies, postcolonial/critical race/Marxist histories that account for gender in some way--those can and have been considered feminist at times, by their authors, by their reviews, by their readers. This has a lot more to do with a claimed or perceived political stance than topic or method, although obviously there is a good deal of overlap.
The distinction that historians who study women draw is instead between "women's (slash gender) history" and "history of women." One of my professors describes the latter quite eloquently as: Find the women. As historians started to pay attention to women over the course of the 20th century, the initial approach was all too often "find the women"--go back to the same sources and tell the same narratives, but just say, "Hey look, a girl!"
The hope, promise, and success of women's history, on the other hand, is that paying attention to women and to gender concerns fundamentally changes not just the stories that historians tell but how we research those stories--methodologies and sources. The foundational theoretical work here is unquestionably Joan Scott, "Gender: A Useful Category of Historical Analysis" (free PDF).
To give a brief example, let's take another famous essay by a famous Joan: Joan Kelly's "Did Women Have a Renaissance?" (PDF link). Kelly focuses on women, contextualized carefully in class context, to question the nature of "the Renaissance" as liberatory early modernity. She writes explicitly "women's history" (176), showing how paying attention to women and the sources that involve them (for/by/about women, directly or indirectly--historians of women are CHAMPIONS of brilliantly creative readings of sources, although Kelly's work here is fairly straightforward) fundamentally reshapes out understanding of, in this case, a period of time/periodization. She studies well-known sources that were nevertheless neglected as not contributing to historical metanarratives, using their attention to women as a way to reconstruct the overall narrative of the period. This is a politicized, feminist argument.
Kelly of course inspired a whole swathe of reactions, including a groundswell of scholarship on Renaissance (in the classicizing Greek/Latin, philosophical sense) women writers like Isotta Nogarola and Olympia Fulvia Morata that paints a very ambivalent picture. (To provide some broader context: there is a raging debate on whether things got better or worse for women as the late Middle Ages evolved into early modernity or 1400-1600. It is enormous, complex, politicized in every way you can imagine, will never be settled, and scholars are okay with this.)
One book I'm going to highlight is Anthony Grafton and Lisa Jardine's From Humanism to the Humanities: Education and the Liberal Arts in Fifteenth- and Sixteenth-Century Europe. This is not a book that jumps to anyone's mind as a history of women, women's history, or feminist history, and a run through the publications of those two scholars won't scream women's libber anytime soon.
But folded into their exploration of education and what it meant to "be educated" is a chapter called, "Women Humanists: Education for What?" Grafton and Jardine use the women Renaissance humanist writers I mentioned above to uncover a dichotomy between the ideals professed by Renaissance humanist philosophy of education and, er, humanism, and the reality. Paying attention to women, and in this case to relationships between women and men (and this includes men's support of these women!), allows Grafton and Jardine to reshape understanding of Renaissance humanism in practice. Women aren't the focus of the study overall; it is categorically not a history of women. But: paying attention to women as women, men as men, and the idea of gender isn't simply writing women into an existing narrative--it actively rewrites the narrative.
I'm trying to elucidate if there is an accepted difference as some feminist histories can overlook capitalism, middle/upper-class women and can anachronistically interpret oppression
It's impossible to make sweeping claims here because women's history/feminist history/history of women are fields made up of individual scholars who evolve over the course of their careers. And then, of course, there is the disjunction between responsible history (in or out of academia) and random Internet clickbait stuff. One of the biggest problems as far as diversity within women's history goes is that it reflects the field more broadly: American and European history are more popular than African and Latin American; there are more sources on rich women than poor ones (which also has a race, disability, etc. implications). White, middle/upper-class Westerners study and write published history far more often than women and men of colour, non-Westerners, etc. But I think a few points are worth highlighting:
From the time we can speak of proper women's history in the 1960s (although Gerda Lerner et alia stood on the shoulders of foremothers and a few fathers who are all too often forgotten in this capacity), the field overall has been exquisitely class conscious, even when focusing (often apologetically) on elite women. Women's history is a direct outgrowth of midcentury social history steeped in Marxist historiography/class consciousness. Lerner and other early women's historians were frequently labour historians. And heck, one of Lerner's first books was of white women who turned their backs on women's suffrage when first-wave feminism chose racism over solidarity. (Yes, she later turned her historical attention to actual women of colour.) I'm not excusing the enduring racism and classism within the field, as noted above, just pointing out that accusations need to be more carefully leveraged.
I'm not sure what you mean by "anachronistic claims of oppression." Responsible, peer-reviewed women's history is responsible history, period. Historians interpret sources. Debates arise when people interpret sources differently. A fantastic example that I hit on earlier is the early modern witch trials. You can certainly find scholars, especially in the 80s and 90s, arguing that these are Oppression of Women, Hatred of Sex, Disgust That Women Have Sex, and so on. But further research, new sources, new methodologies, adjusted narratives (including studies of contemporary women unrelated to witchcraft, and of men related to witchcraft) have nuanced those claims. That doesn't mean that women were not targeted FAR more often than men (85:15 overall), or that female gender played no role. But it means that new sources and new methodologies give us a clearer picture. Ruth Mazo Karras and Dyan Elliott are both historians of late medieval sexuality (and like a gazillion other things) who are at the tip-top of the field, yet they have vastly different perspectives on the "status of women" in e.g. 15C. (And I've watched them participate in a roundtable-type discussion together and laugh over this. While crocheting, because like 80% of women in academia crochet).
It is always important to be critiquing one's own scholarship and one's field to see how it can do better. Whether that is for political purposes as a feminist, scholarly ones as a historian, or because someone sees no practical distinction between the two, it's necessary. But it's also important to recognize that we're not the first ones to do so, and to use the insights and lessons of previous scholars.