I have both of the programs loaded (trial peroid to see if I like them). If I want to copy a DVD (the dvd being one I legally own), I use cloneDVD and AnyDVD will run in the background, without me having to start it, to remove any copy protection, correct?

Thanks

correct, once installed, unless you tell it not to, AnyDVD launches automatically when the PC is booted up, so it sits in the background un-noticed, Clone DVD will then copy a copy protected DVD