My mom once told me that cologne is oil-based, so it is stronger and lasts longer, while perfume is alcohol- or water-based. I know this was definitely true for her favorite scent that she used to wear all the time. She would only buy the bottles (or pulse points, or powder, etc.) that said cologne because it lasted longer (and therefore was a better deal). About 5 or 6 years back the company that made it discontinued the scent, but there was such a strong response they brought it back, but only as a perfume. I noticed that the perfume, while it smells just as good, wasn't nearly as strong and didn't last as long.
But since perception drives reality, and the market, I think some companies have gone more with the common belief that cologne is masculine and perfume is feminine, at least with the more largely available scents. Higher end, more expensive scents may still be described by the old rules, but I've never looked that closely at it.