Yes and no!
It really just depends on the program you are using.
Typically Save to PDF is supported in very few applications (either by Adobe or by the program maker). It creates an enhanced PDF file that typically has additional features - such as if you had hyperlinks in a document, they will be preserved.
Printing to PDF is different as it is for ANY program that can print. It basically redirects what would come out of your printer into a PDF file. In the above example with the hyperlink - In Microsoft Word, it would typically just come out as blue text (as it would on physical paper) unless you manually format it!.
That being said, I believe that a few PDF printers do try to preserve some enhanced features, however the above should be typically true for most.