When you are looking at a PDF in a browser, using the Adobe Reader add-on, there are two different apps you might be talking to. The browser, itself, or Adobe Reader.
To be sure you are talking to Adobe Reader, use the Adobe Reader toolbar, which appears over the document if you hover. Then you are certain that the print (or save) is done by Adobe Reader.
If you use the menus or the browser toolbars, you talk to the browser. In an ideal world the browser says "I don't know how to print this" and has Adobe Reader do it. But that doesn't seem to happen. Sometimes it fails, or you get a screen grab printed. Over the years all sorts of things have happened, rarely good.
Worst of all is Ctrl+P. It seems to be pot luck whether Windows gives the shortcut to the browser or the add on.