Oh, I see. Maybe you are actually talking about copying files you've already merged and upgraded. It wasn't clear from your first posts.
The upgrade instructions do talk about setting up your site in a separate folder for staging the upgrade and preparing all the files for use on the live site.
Whether you want to rename a folder to take the changes "live", or simply copy all the new files into the existing live store's folder, is up to you.
When I'm doing upgrades, I do all the testing with a copy of everything from the live site onto a separate server, not just in a separate folder. Then, once I'm happy that it's all working fine on the test site, I repeat the upgrade on the live site, including copying all the files into the new site. It's not "necessary" to have a "/store/" and "/store_new/" folder to rename, although that will work if your store is actually in a folder named "/store/".
If your store is in the "root" of the site (ie: /index.php is part of your Zen Cart store) then you could do your testing and staging in a subfolder (called anything, whether store_new or store or bobby or testing ... anything) and then copy all the files into the main folder when ready to cut over.
There are lots of ways to do it. Pick one that works for you. But don't skip the merging of customizations from old to new. That's the part most people get lazy in, just because it takes time and feels daunting.