This error may show during fullbackup / cpmove file restore in WHM hosting panel.

DOMAIN CONFLICT: * owned by * - the copy failed!
It can mean that cpanel account mentioned in error message has same domain that is in account you trying to restore. Discover by whois which account is used to serve websites data. Keep backup of the cpanela ccount and remove Addon domain from account that dont serve domain + make new backup without that domain. This backup restore and check that mentioned website is working after nameservers change.