lxc publish doesn’t retain the instance’s configuration, where as lxc export does.
Also lxc export will also backup snapshots, that lxc publish does not.
So lxc export is for backing up a particular instance so it can be restored in the event of data loss.
lxc publish isn’t for backup at all, and is for publishing an image from an existing instance so it can be used to create one or more instances from it.