Hi,
Up to Lion which had iChat 6 what you say about which app did what is true.
At Mountain Lion the App on the Mac became Messages.
This added the iMessages account. (You used your Apple ID for this).
This could then iMessage to Macs with an iMessages account or an iOS device such as an iPhone.
Basically a piece of iOS software was added to the iChat App and the name was changed.
iMessages gets talked about in terms of a type of Message, the account type and the Service run by Apple for iPhone, iPads and Macs and some iPod touch devices.
So... Macs and iOS devices can iMessage
The iOS version on the iPhone could send iMessages to Apple devices (with iMessages accounts) or if the device was either not in range to do iMessages or was an non Apple phone it could send SMS/MMS messages.
By the time we get to Yosemite (OS X 10.10) and iOS 8.0 on the iPhone then the ability to link to SMS/MMS messages from the Mac is added as an ability of the iMessages login.
The devices are paired by enabling "Text Forwarding" on the setting on the iPhone > Setting > Messages which in turn triggers a slide out on the Mac which shows you a code number to enter back on the iPhone.
The Messages app can still do all the things that iChat could do as far as connections an Chats are concerned (iChat Theatre has gone from Video chats and the interfaces have been changed somewhat and Text Formatting has gone).
If you mean since the 7th November the app has sent no messages of any sort I still need to be certain of which type of Account it is.
If it is an AIM chat it will say in the text field of the chat

Or iMessage

However the AIM service also allows SMS forwarding to specific carriers in the United States as iChat could always also do.
I have a spoof "Buddy" in my AIM Buddy List that is a phone number

You have to add the +1 to the number (the app will format them for you)
So in certain circumstances the Messages app can now send SMS/MMS messages two different ways - via iMessages with a paired iPhone or the previous "iChat Way" using an AIM Buddy list.
However this is recent (since the iOS 8 release once you have Yosemite) and if you have been doing it "for years" you have been using the AIM method.
I would try dis-Enabling any AIM account you have in the Messages menu > Preferences > Accounts and then Quit the app.
On Restarting the app re-enable the account.
If you want to change use of a Contacts or Buddy's phone Number to iMessages rather than AIM then you need to change the set up in their Address Card in the Contacts app as the phone number may be listed a Buddy and not a Contact (iMessages) option.

10:02 pm Sunday; November 16, 2014
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