Transferring install on same godaddy server to a new domain

I have two domains registered and activated with godaddy.com. Currently my zencart is installed as https://www.andrewreach.com/zencart. I'd like to migrate it to my other domain https://www.vintagepalace.com and want the address for my store to be the same (not https://www.vintagepalace.com/zencart).

I'm not sure if these instructions I want to move my Zen Cart installation to another host or a different server (see link below) applies also to what I'm trying to do since the zencart I currently have installed and where I want to move it to are on the same server.

http://www.zen-cart.com/content.php?142-i-want-to-move-my-zen-cart-installation-to-another-host-or-a-different-server

Thank you.

If those two "domains" are in separate hosting accounts (ie: when you use FTP to login to manage files in the sites, it requires different passwords in your FTP program), then you need to follow the instructions in the article you quoted.
GoDaddy has thousands of servers, so while you may have two domains with them, they may very well be on completely different servers. Even if they're not, you still need to follow the article.

By "FTP program", I am NOT referring to their "file upload tool that runs in your browser".

If they're truly in the SAME hosting account, (ie: use the SAME login for your FTP program), then you could try simply updating the domain names and paths in your 2 configure.php files if you've got a solid handle on how those settings work. If no, simply follow the tutorial you quoted so that the process will create new configure.php files suitable for the new domain.

Thanks so much