What is the difference between to File > Export as PDF and File > Print > Save As PDF?
"Save as PDF" is essentially a digital copy of what you get if you were to print a specific page from Safari. This includes extra headers/footers that include the date, webpage, number of pages, web address, etc.
"Export as PDF" is a simple snapshot of the page as is and does not include all of those extra details.
From the few pages I've compared the differences with these two options, Export as PDF tends to retain more of the formatting details whereas the Save as PDF option can cause the page to look slightly different.
Export as PDF is a Safari-specific feature. The print-option is system-wide. In the case of Safari you'll also have your usual print-features that you can check or uncheck here such as printing the backgrounds as well as headers and footers
One difference I have noticed, and it's a big one, is the page size is different in the Export as PDF rather than going to the Print and Save as PDF option. I didn't know about this and was surprised when this happened. It is very annoying but this is the difference I see between the two options. Using the Save as PDF option from the PDF pulldown menu in the Print dialogue gives an A4 sized PDF if the paper size is set to A4. Using Export As PDF gives something different, that changes according to the website thou are exporting.
(My answer below applies to Safari 9.1.1 on Yosemite.)
Using "Print to PDF" will apply whatever style sheet you have activated. If you are good enough with CSS to hack your own style sheet for printing, you can get the output look as you please: you can change the page sizes (even to very custom, non-standard ones), margins, font faces, font sizes, etc.
To apply the CSS you want, go to:
Preferences... => Advanced => Style Sheet => (<Other...> || <existing_sheet.css>).
For using "Export to PDF" I've found no way to influence the look and feel of elements on the PDF, not even page size or margins (for me it's always A4 portrait). For example, the mono font seems always to be Courier (while with the "Print to PDF" approach I could easily change it to Menlo, Monaco or Source Code Pro via CSS).
There may be a way to influence the "Export to PDF" outcome by using some secret
defaults write com.apple.Safari ...command lines, but I've not yet explored this path.