Butchery in early modern Europe was a little unusual, as a craft: butchers' guilds typically required meat to be priced and sold by weight rather than specific pieces or cuts (a visitor to Paris at the end of the 17th century was surprised to find the opposite was true there; the Paris government took steps to align with the rest of Europe a few decades later). Regulations on butchers tended to focus on (a) waste management and cleanup, an enduring problem, and (b) what constituted the poorer levels of meat that could still be sold and consumed. On both sides of the Atlantic, the ideal practice was to buy a larger "piece" of meat from the butcher and worry about "cut" individually.
That said, the bones and joints of a cow dictate rough guidelines for butchery. In cookbooks over the course of the nineteenth century, we can see the names for joints start to align with cuts of steak based around them, although there is still some variation in joint names. But cookbooks and household guides also stress the diversity of specific cutting styles based around the joints:
The Manner in which a Side of Beef is cut up in London is shown in the accompanying engraving. The custom varies in different parts of the country, and in some places no difference is made in price between one joint and another. This, however, is of rare occurrence. (edit: fixed the name; Isabella Beeton, Mrs. Beeton's Book of Household Management, 1861)
But by the time Beeton published her handbook, as you can tell by her reference to London, that diversity was becoming less individual and more regional. David Landon, "Feeding Colonial Boston," analyzed cattle bones and found that the gradual homogenization of butchery patterns in that specific city aligned with the introduction of the butcher's saw as the primary tool from the second quarter of the 19th century. With greater urbanization, butchers were more often responsible for producing meat cuts. They were catering to a local market familiar with local customs. Interestingly, this era of "regionalization" seems to correspond with both the attributions and the popularity of some of the mythical/disputed etymologies for particular (non-joint-related, like porterhouse) steak cut names.
American cookbooks continued to stress the importance of regional (generally by city) diversity into the mid-twentieth century. The rise of industrial slaughterhouses and meat-packing actually didn't change this! Meat was shipped in large chunks from slaughterhouses to butchers (or you can find online butchery purists who insist that this was the fall of the butcher and the rise of the "meat cutter").
The stabilization of steak cuts in America is a post-World War II innovation. There were a couple of steps involved: homogenizing the available cuts and convincing consumers this was a good thing. First, the postwar period saw major changes in the way steak got from cow to household table. Electricity and (OMG) refrigerators meant people could buy meat more days in advance rather than visiting a local butcher for the "daily meat." Instead, they went to supermarkets and bought cellophane-wrapped pre-cut meat, that had been mass-shipped by truck directly from meat-cutting plants now part of slaughterhouses. Companies, in other words, could fetch a higher price for their product by cutting out the butcher middleman.
That part of the story is British as well, but I'm not sure how much the second part is. The postwar middle-class prosperity complex, suburbanization, and corporatization of American dining catalyzed massive growth in the American franchise restaurant. With the changes in meat shipping, too, steakhouse chains became economically viable for the first time. (There is way more scholarship on American steakhouses than I would ever have dreamed.) Two factors contributed to the consolidation of cuts. First, "branding" or selling a theme--mostly "The West" or "Texas"--spread specific cuts of steak to new regions as steakhouses became national instead of city chains. Second, steak was still a prestige meat and relatively expensive compared to hamburger. So steakhouses, buying their cuts of meat in bulk, had to streamline their menus down to just a few cuts of, generally, cheaper steak in order to stay profitable.
I'm a vegetarian and there are probably some wild inaccuracies in here from the point of view of actually picking up a slab of steak, but that's a general overview of the consolidation of American steak consumption from the colonial Wildwuchs to the menu of Outback.
You may also try r/CulinaryHistory (they renamed r/foodhistory)
Just a friendly reminder to OP that /r/askfoodhistorians also exists and might be a good place to find someone who can answer the question.
AskHistorians has surprised me before but I think this is a very very specific question. You might consider to post it also on https://www.reddit.com/r/Butchery/ Seems there are pro's there who might be able to answer you.
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Followup: Portuguese and Brazilian meat cuts (for beef at least) are also different from each other. Are the Lusosphere reasons similar to the ones in the Anglosphere?
Others have mentioned certain alternate subs for this question, but please also consider /r/AskCulinary, which has over 100K subscribers and many enthusiastic experts.