Hi,
Ok.
I will restate this as I may not have been as clear as I could be.
The Messages app as it is now will do two forms of Video and Audio chat and Screen Sharing.
This does depend on which Account you are using in the app.
iMessages
By default before any set up the Messages app will display two items in the Accounts List (Preferences > Accounts).
One is a place for your iMessage ID which is based on an Apple ID that in turn may or may not be your iCloud ID.
The Second is the Bonjour account which is normally not active (this will find other Bonjour computers set for Messages or iChat and their Bonjour Accounts).
For Video the iMessage account invokes FaceTime as it does for Audio Chats.
That is to say that for connecting to a Contact for Video, starting at the Details item top right of the Chat Window the app will cause the FaceTime app to start.
Since Yosemite (Both Mavericks and Yosemite both refer to the Messages app as "Version 8") you have also been able to Invoke the Screen Sharing app from the Details Drop Down, once the System Preferences > Sharing > Screen Sharing has been enabled on both ends.
Using this method causes the Messages app to supply all the connection details to the Contact that you would normally enter manually via Finder > Go Menu > Connect to Server and enter VNC:// as the lead part of the address.
So to summarise:-
First Enable this:-
Next start a conversation with an iMessages Contact.
Then use the Details item top right and select the Screen Sharing icon.
AIM, Jabber and Bonjour (As in those account present in iChat before it became Messages)
To Enable you need to set the item in Video Menu.
This is a pic for iChat 4 which does have some references to items no longer present like Record Chat.
As Stated earlier AIM, Jabber and Bonjour connections fro Video and Audio plus Screen Sharing are handled by the app.
Buddy Lists show whether the Buddy can Video or Audio Chat by the icon.
The Icons across the bottom of the Buddy list show the one for Screen Sharing.
You can select the Buddy (as I have here) and either use this icon or the Buddies Menu.
As I said earlier though there is an issue with this method at the moment.
Screen Sharing app
This can be invoked in several ways.
One is to use the Shares in the Finder's Side Bar and then the Screen Share button
Another way is to use the Finder > Go Menu > Connect to Server and enter VNC:// in front of the IP (normally it would be SMB for windows capable shares or AFP for Apple Specific ones)
This can be used over the Internet. The IP has to be the Public one of the other end (the one their Router or Modem gets from their ISP)
The Router then needs to Forward the port that this data is on to the Computer involved. The port is 5900. (same as Apple Remote Desktop as the app is part of that).
Unlike the two methods in the Messages app this will not include an Audio chat "alongside".
NOTES
In System Preferences > iCloud there is no references to the Messages App.
This means that you cannot set the iMessages account from here.
However in Messages you can use your Apple as a Valid AIM screen Name due to a 15 year deal Apple did with AIM to allow Apple Issued email IDs to be valid Screen Names.
This applies to the Apple IDs that end in @mac.com, @me.com if linked to iCloud and to @iCloud.com one themselves.
This does mean that you can enter your Apple ID in two places in the the App which does render the phrase "iCloud Account" not particularly useful.
The same is true of an Apple ID if it happens to be your Google ID or a Yahoo one.
If like me you have an Apple ID that was linked to MobileMe or to iCloud very early on when you got an @me.com ID as well you can use the @me.com and @icloud or even the @mac.com IDs as separate Screen Names
That is to say my Apple ID which is linked to iCloud has three variants.
I use one for iMessages and have two other set as Screen Names
I hope that makes it clearer.
8:48 p.m. Tuesday; September 15, 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