HI,
Whilst the iMessages and Text options are both based on the Apple ID the iMessages side requires the app can login fully to the iMessages servers.
The Text Forwarding from the iPhone of SMS messages only requires the iPhone can get SMS Messages, is using the same Apple ID and is on the same network.
(I.e. the two systems are separate from each other but are linked via the Apple ID to link them but need the iPhone to be connected to the carrier)
Any issue with the iMessages servers and you lose them whilst you may still maintain SMS abilities.
As I have said before, at the OS X 10.8.2 update Messages 7.0.1 (as it was updated to in this update) then needed the Mac's Serial Number to be present and this was used to create a unique identifier called the Auth Token based on the Apple ID in use.
At this point if the Serial Number was not present a pop up appeared telling your to contact Apple Support and a code number for your error.
Now we appear to have related but silent failures (It looks logged in but will not send).
These seem to fall into two groups:-
1) the Contacts turning red and getting the messages that they "Are Not Registered with iMessages" ( A bit like not getting your Buddy list on other services)
2) the iMessage appearing to be sent but instantly getting the "Not Delivered" error alert.
Some checks have helped some people:-
Date and Time settings in both Mac and Router as the login and iMessages are Time Stamped.
Check the AppleGothic font is Active, not duplicated and Validated (File Menu in the Font Boot app).
Checking DNS settings in System Preferences > Network (Listing the router's IP is not always good enough)
A PRAM/NVRAM reset has been known to help some (Restart the computer holding down ALT+CMD+P+R keys until you have heard three Start up bongs then let the start up continue.
A Safe Mode boot have worked for some.
Both these reset some things you can't reset other ways.
Deleting the Auth Token and restarting the app can work but is in the rare category.
Deleting the com.apple.imessages.bag.plist (the listing the servers) and the IDS ****.madrid.plist that list the Apple ID and the alternatives can help.
You have to re-enter the Apple ID if you delete the second one.
Apple do seem to be working on this.
However that means finding the cause and not resolving the symptoms that seemed to happen earlier on when Level 2 support people were resetting the iMessages servers regarding the Apple ID used by the Mac.
It tends to get bumped to the Engineers and anything to resolve the issue tends to be taking a back seat.

7:26 p.m. Sunday; June 14, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad