Nope, they don't have anything to do with each other as far as I know. A cookie is a small file that websites store on your computer to save your preferences for that site and such. Spyware records your information and sends it back to a server.
As far as I know, a cookie can only tell the server it originated from the details you have already given it through your browser at best. Whereas spyware or adware can get information from your computer and give it to whichever server it is set up to send the information to.
Don't worry about spyware at all. Each time you want to run some sort of spyware program, instead go into Disk Utility in your Utilities folder in Applications and repair permissions. It has nothing to do with spyware but it's a pretty cool way of making you feel like your helping your computer (which you are to an extent).