When you are printing to a PDF using either a PDF Printer (Windows) or Built-in Functions (Mac), they are attempting to emulate the output of a physical printer. As a result, you can often get undesirable elements and results including crop marks, registration marks, bleed, margins, color bars, and other printer marks. In addition, saving to PDF will maintain a CMYK profile which can also shift your colors for export.
When you save as a PDF using Illustrator's native function (via File > Save As and using the drop down switch to select your artboards), you are generating a PDF with Illustrator-like functionality. In addition, you can control which artboards you want to export, what color profile to use, archival profile, add a password, and even retain the Illustrator layers and editability with one check box!
For an extra tip, did you know that you can open AI files in Acrobat? Just Right Click > Open With on the file and open it in AI. All of your artboards are retained, all of your sizes, all of your settings. And yet, it acts like a PDF. Cool, no?