Syncing With Icloud (default sync items and notes etcetera)

The contacts should be created in Mac address book , under section All iCloud , select the contact ( use command and A keys ) , copy it ( use command and C keys ) , and paste ( use command and V keys ) to a group created .

Groups don't sync , this will stop syncing those particular contacts ( having three notes ) to the second Mac .

See the article Change settings in Notes on Mac – Apple Support

Enable the On My Mac account

Store notes on your computer using the On My Mac account.

Another article About accounts and folders in Notes on Mac - Apple Support 

• You can only move or copy locked notes between folders in your iCloud and On My Mac accounts (and you may need to unlock them to do so).

Right click on the note in iCloud section and move to " on my Mac " this will remove the iCloud notes and move to the folder in " on my Mac " , the other Mac that is signed in with same Apple ID and password on the same network will remove that particular note , apply in the same way for all other notes .

The Mac should be upgraded , its optional to sync all items like desktops and documents , notes ....with iPhone and other devices .

Syncing will occur fast when devices are connected with high network speed , specially when connected with usb cable Intro to syncing your Mac and your devices - Apple Support

Sync content between your Mac and iPhone or iPad - Apple Support