Move Time Machine backup to new drive

I have been searching the forums and haven't been able to find the answer to this yet.

My Time Machine backup is on an external hard drive. I want to move it to a new drive and get rid of the old drive. But I can't find any information that says how to do migrate from one drive to another. Can I simply copy the Backups.backupdb folder over to the new drive? I'm guessing it's not that simple.

Also, about the "Ignore ownership on this volume" checkbox. I'm confused by what I've read in the forums because it's kind of like a double-negative. Once & for all, for this new drive do I want it checked or unchecked? And why?

Thanks for your help.