Hi knarfrh60, the first thing I would do is back up all your contacts in AddressBook on the iMac: in AddressBook go to File > Export > AddressBook Archive. Keep it somewhere safe in case things go wrong.
Next check your iCloud Settings on both the iMac and the iPhone. The contacts on the iPhone and the iMac shouls be identical if your settings are correct, so it is likely they are not. ensure that on the iMac in System Preferences > iCloud:
1. that you are logged in, and
2. contacts are checked.
I'm just trying to see what's loaded into the system. Currently, it is possible to see the screen on my iPhone with them but on the iCloud website and using Contacts/iMac it does not show.
Did you have a suggestion on how I could view the labels created on the iMac? I understand that the iCloud account is syncing on the iPhone and website.
On the iPhone, try going to Settings/iCloud and unchecking the sync Contacts and then checking sync again. Check and see if they now appear in iCloud.
Apple support articles: