Messages app and What it Can do: Yosemite.
Hi, (Edit 2)
Messages is one of Apple's communication apps (the other being FaceTime).
It can have 5 types of Accounts.
When you open it for the first time it will ask you for an Apple ID.
Once this is set up the Messages app > Preferences > Accounts show two default accounts (you can never delete these one Disable or remove the Apple ID in the case of the iMessages one). These are the Bonjour account which by default is disabled and the iMessages account. Bonjour works to other Macs on your LAN.
After that you can add AIM/AOL accounts, Jabber accounts via the "Other" option and Yahoo.
The Choice dialogue box also offers Google. This is a Jabber server but it does not conform to the standard Server naming protocol so it gets it's own choice.
Some History to explain a little further.
Previously (before Mountain Lion) the App was called iChat.
iChat 1 was a Text only app which worked with AIM and Bonjour (although it was called Rendezvous back then). It was not actually called iChat 1 either.
iChat 2 brought Video and Audio only chat abilities.
iChat 3 added Jabber. (some resetting allowed it to work with Google).
iChat 4 adds 4 way (you are 1) Video chats and 10 Way Audio Chats and Screen Sharing in AIM, Jabber and Bonjour.
At this point Bonjour, AIM and Jabber accounts can Video or Audio Only to other Mac. The AIM account can also Video to AIM on PC users.
At iChat 6 a Text Only Yahoo option is added. This is in Lion (OS X 10.7.x)
The Numbering continues in Mountain Lion when the App becomes Messages (version 7) and adds the iMessages account.
SO that is:-
AIM,
Bonjour,
Jabber (including Google and Facebook Chat)
Yahoo and
iMessages
iMessages is Text only in Mountain Lion and Mavericks. (when you can see the Video icon when chat to a Contact it invokes the FaceTime App).
You can send certain files and Pic-in-chats.
In Yosemite it can Screen Share but unlike the AIM, Bonjour and Jabber accounts it invokes another app like it does for Video and Audio Chats.
In this case it is the Screen Sharing app which needs System Preferences > Sharing > Screen Sharing to be Enabled.
With iOS 8 the iMessages account can sync iMessages to and from iOS devices.
It can be set up on the iPhone to "Text Forward" SMS messages to the Mac (the Mac and iPhone need to be on the same LAN. Starting the process on the iPhone causes a code to appear on the Mac which needs entering back on the iPhone). The Text Forwarding effectively Syncs SMS Messages as well.
Bonjour is Text, Video, Audio Only and Screen Sharing to LAN based Macs at your location that are using Messages or iChat. If you LAN is divided into Subnets then only your subnet can be seen.
AIM is Text, Video, Audio Only and Screen Sharing to other Macs using Messages or iChat. Certain Apple IDs ending in @mac.com @me.com if linked to iCloud and @icloud.com will also work as valid AIM names if the password is 16 characters or less.
It can Text to several other Mac based AIM clients and to PC version of AIM and web based AIM Logins.
An AIM account can also do SMS but ONLY to certain Carriers in the United States.
Jabber including Google and Facebook Chat is Text, Video, Audio Only and Screen Sharing to other Macs. Again it will Text to various other logins for those servers. There was a PC app called GoogleTalk that you cannot Video to but you can text chat. The same as you can text chat to someone with Facebook Login and the Chat part enabled.
Yahoo must use a Yahoo ID. (The server works with several different type of valid ID not issued by Yahoo)
It is Text only (not even File Transfers that applies to the others).
Video chat can be up to 4 people in the Bonjour, AIM and Jabber accounts.
As I mentioned early it invokes FaceTime in the iMessages account to Video and Audio Chat and invoke Screen Sharing app to Share Screens and the Yahoo account is Text only.
Audio Only chats can be up to 10 people in those same three account types.
Screen Sharing is only 1-1 but works in the AIM, Jabber and Bonjour Accounts. It include an Audio Only chat along side the Screen Sharing.
NOTE AS of August 2015 there appears to be a problem with this service (it is run though an Apple Server called SNATMAP) and a "fix" is being looked for.
NOTE.
In System Preferences > Sharing the Screen Sharing and Remote Management cannot be Enabled at the same time.
Both use the Apple Remote Desktop engine (as does the Screen Sharing in the AIM, Bonjour and Jabber accounts).
This form of Screen Sharing can be started from the Finder > Go Menu > Go to Server and starting the link VNC:// rather than SMB (Windows) or AFP (Apple File Protocol).
This Starts the Screen Sharing app that is actually in Hard Drive name/System/Library/Core Services/Applications in Yosemite.
In the iMessages account it includes an Audio chat.
Editted 9:31 p.m. Wednesday; September 9, 2015
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