Always get in the habit of considering the .ai format your "working file" with things like open fonts and such, and final/print ready files should be saved as an .eps, (with outlined fonts) or at worst a .pdf.
There are very specific reason for this, but I just give you a brief overview... EPS stands for "Encapsulated Post Script" which means it carries printer data, including color profiles! This has been the universal de-facto standard for years and years in the print industry for pre-press work.
Also, your screen preview and printed images look different from one another between .ai and .eps.