Pantone colors follow the professional printing ink colors, which more closey follow CMYK. Any "web safe" color will always be RGB because your monitor cannot display anything but RGB. So, the problem you have is that printing house inks have been around a lot longer than computers and what you have managed to get is a close approximation for your screen display. As far as printing your logo on an inkjet printer and it being "lighter" in color tones, this is just a matter of not having your monitor "color balanced" with whatever graphics application you used to create your logo. And not all graphics applications allow your to match your monitor with RGB colors and your printer. In all likelyhood, you'll end up with a logo to print (for letterhead and other business forms) and one for the web.
There's always a better way. The fun is trying to find it!