What does “high resolution” mean?
Is the small jpeg file “high resolution”? Of course, it is 900 pixels and printing it at 300 pixels per inch, you are only getting 3 inches. So it is not a resolution you are asking, but the print size. When viewing an image on the web, the browser does not display at 300 pixels per inch, but maybe 90 pixels per inch (measure your screen resolution if you are curious about what it is, but every screen is going to be different! what I do know is it is NOT 300 pixels per inch!) So the 900 pixels on the long side of the small jpeg file will be 10 inches on your screen! See this article if you are interested in more detailed explanation.
So a medium size jpeg file has a lot more pixels than the small jpeg file, and you can print bigger at photo quality. But they are all “high resolution”! You should care about how many pixels are in the file, the more pixels, the more inches you can print as a photo.