In Safari "Export to PDF" looks different then "Print as PDF" - Why is this?
Well, I know this is an older question, but I came upon it and thought I would answer...

There are two things that can be different here -- one, as is noted in the question, is the special set of styles used for printing. This is set up on the website you are looking at, and is not something you have control over. The second are the print options. I think by default printing of background images and colors is turned off, and it is possible to make other settings too. These are controlled through the print dialogue.

The automatic print stylesheet is a a pet peeve of mine. I've always thought a better solution was to offer a button to let visitors choose to format the page for print, rather than doing it without their control. I always want to default to giving users more control rather than taking it away.

I would assume that if you set up a special user stylesheet to be applied to all pages in the Safari preferences (normally done for folks with needs for special display characteristics such as high contrast or extra large type), those styles would be applied when printing as well. I haven't tried that out, though.

TLDR: if the website has their CSS set up to serve special styles when printing, there isn't much you can do about it. While you do have control over some elements of printing, such as printing of background colors and images through the print dialogue.