OK, thanks for the additional information.
I think the issue is difference in OS X and iOS versions as far as how iCloud syncs. When Apple moved to OS X 10.11 El Capitan, they upgraded iCloud Notes. If you performed the upgrade to iCloud Notes. they will no longer sync with devices running OS X 10.10 Yosemite or iOS 9 or earlier.
Upgrade your Notes app
If you upgrade to 10.11 El Capitan or 10.12 Sierra, then the Notes will sync again with your Mac. You can verify which Notes are syncing, by logging into iCloud and comparing the Notes against your Mac and iPhone.
Hope that helps,
C