Hi,
More info.
The app was built on it's forerunner, iChat.
Many Menu items reflect this.
Using one separated Buddy List and the Buddies Menu you get this:-

The Highlighted Buddy ("Me at Home (PC) Johns") activates some of the items in the Buddies Menu.
AS this Buddy is already Added then I can Remove him.
The FaceTime options are sometimes active if the Address Card has an Apple ID or potential iPhone number listed.
My EL Capitan version implies at this point that this is the only option although Video from within the App is possible with AIM to AIM and Jabber to Jabber chats if the person is also using a Mac and iChat or Messages.

I only know this chap via AIM.
iMessages conversations are with Contacts (not Buddies) and you have to use the Main window and a started conversation to move to Video (using FaceTime or Audio (Using FaceTime) or Screen Sharing (via the Screen Sharing app)

An option is to use the Details item to the top right of the chat/Main Window
Apple makes the distinction that iMessages uses Contacts and Buddies have Chats.
The Buddy Lists were already there in iChat but something like a buddy list was not use to chose the Contact to connect to.
Whilst a Contact may also be a Buddy with multiple account type IDs and Screen Names on their Address card the distinction remains for chatting purposes.
As AIM allows the Username@serverOrEmail.com names as in "username@iCloud.com" then issues about adding a Buddy name or ID to a Buddy List can ensue.
All Jabber names are Username@jabberServername.com whether they offer email services as well or not.
Yahoo ID are Username@yahoo.com (Buddies in this list can also have other Valid Yahoo IDs)
Therefore it is possible to add and email style name to any Buddy List that will accept it.
The "buddy" will always appear Off line though.
GoogleTalk is a Jabber service.
This means you can add Jabber Buddies to any Google Buddy list you have or add Google Buddies to any Jabber Buddy list you have.
You have to set up Yahoo using only a Yahoo ID.
However the service does allow several other ID types as valid names. (I don't use it much so I am not sure but I think MSN were/are one type).
Video and Audio Chats.
iChat could do Video and Audio Only chats plus Screen Sharing for AIM and Jabber accounts when both ends are on a Mac.
The Screen Sharing was essentially an audio Chat with a VNC connection alongside and making use of the Apple Remote Desktop (ARD) engine.
This was all in App and opened up separate windows to do so.
You could not Video at the same time as Screen Sharing. (You could "Convert" from video to Screen Sharing but not the reverse)
The Messages could have used the same method for the iMessages account and made it compatible with FaceTime (or iPhones and iPads for instance).
However Apple decided that an iMessages Account would invoke FaceTime for Video And Audio chats to Contacts.
it does mean you are sure to connect to an iOS device as well as other Macs but you lose the 4 way Video chat or 10 way Audio chat ability that the iChat method has.
The Original (ver 7) of Messages could not Invoke FaceTime.
Audio was added later.
In Yosemite the ability to Invoke the Screen Sharing app was added.
This needs the System Preferences > Screen Sharing to be On and allowing anyone. (the listed name are normally Mac Users Accounts on your Mac)
iMessages Screen Sharing (to keep the idea simple rather than listing the invocation all the time) is Mac to Mac only.
The Screen Sharing app is actually part of the Apple Remote Desktop.
If your Work Computer has your Home Computer's Mac User Account on it (in name only if you like) then you could allow just that Mac User account to Share Screens. (the Authentication would be the password for the Mac User account on the work mac (And vice versa).
In most cases you are not sharing with someone who has a Mac User Account on your Mac hence the setting in the Sharing Preferences being set to Anyone.
Of course there are potential security issues although you can end the session pretty quickly if people stray away from what you agree.
The Screen Sharing App method (iMessages Screen Sharing) also has an Audio component.
Lion only has iChat 6 so it cannot do iMessages Screen Sharing.
It will only do it with an AIM or Jabber ID to an AIM or Jabber ID on your home computer (that's AIM to AIM or Jabber to Jabber).
iChat 2 Pictures http://www.ralphjohns.co.uk/versions/ichat2/ichat2pics/index.html
iChat 3 adds Jabber http://www.ralphjohns.co.uk/versions/ichat3/ichat3pics/index.html
iChat 4 adds multiple Video and Audio chats http://www.ralphjohns.co.uk/versions/ichatvers4/ichatvers4pics/BuddyList/BuddyLi stIndex.html
Not a lot changes until Messages which is called Version 7 and keeps the same Numbering.
Mavericks and Yosemite have different version but both are called Messages 8
Messages 9 appears in El Capitan (and sub set numbers at OS X updates reappear)
Messages is at ver 9.2 at OS X 10.11.4
Hopefully I have untangled it for your somewhat.
iChat builds form a AIM only app to include Jabber and later Yahoo at iChat 6
Along the way it adds Jabber, then 4 way Video and 10 Way Audio Only chats and Screen Sharing (although not for Yahoo) (plus the Video effects)
Messages 7 adds the iMessages account which uses Contacts and not the Buddy Lists (the Buddy Lists remain).
Messages in Mavericks tidies things a bit.
Messages in Yosemite offers better integration with syncing with an iPhone and Allow SMS forwarding.
Basically more and more functions are added.
Some are lost like iChat theatre.
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10:22 pm Wednesday; March 23, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
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