Remote Management vs. Screen Sharing

You are correct, VNC is a simpler version of Remote Desktop (note: Remote Desktop uses the VNC protocol in addition to adding a lot more features)

Remote Desktop offers more management features; ability to black out host computers screen, push updates, file transfers etc (think TeamViewer but by Apple). http://www.apple.com/remotedesktop/

VNC doesnt have any of these options, its just a simple way to access a remote screen.

Remote Login allows you to SSH to a remote computer (command line - you dont see the remote desktop)

eg You may want to run a command on a remote computer, you could connect using VNC and open terminal or instead you could remote login via SSH and run the command without actually interacting with the screen of the remote computer

Updated to include @Wheat Williams notes below

I found the following code in a file I didn't open for a long time. It enables Remote Login on a remote device. Save the script somewhere (from now on referred to as /path/to/script/). Copy the script to the other device.

tell application "System Preferences" to set current pane to pane "com.apple.preferences.sharing"
tell application "System Events" to tell process "System Preferences"
    click checkbox 1 of row 6 of table 1 of scroll area 1 of group 1 of window "Sharing"
end tell

This enables remote login. Now, to disable remote management and enable screen sharing, use the same script, but remove the 3rd line and add these 2 lines:

tell application "System Preferences" to set current pane to pane "com.apple.preferences.sharing"
tell application "System Events" to tell process "System Preferences"
    click checkbox 1 of row 7 of table 1 of scroll area 1 of group 1 of window "Sharing"
    click checkbox 1 of row 2 of table 1 of scroll area 1 of group 1 of window "Sharing"
end tell

To copy this script on the remote device, use scp (secure copy). To use scp type
scp /path/to/script username@IP.of.other.device:/some/path
OR
scp username@hostnameOfDevice:/some/path/
The second option (using the device hostname) requires that the devices are on a computer-to-computer network, so it will not work on a normal wifi network. You will see a prompt requesting the password of username. When you type the password, you will not see any text appear (obviously to prevent people from seeing the password).

Once it is copied, remotely log into the device:
ssh username@IP.of.other.device
OR
ssh username@hostnameOfDevice
Again, the use of the hostname requires computer-to-computer network. Once logged in, run the script using osascript /some/path/theScript.scpt (remember that using scp we copied the script to /some/path, this will be different on your device). This will disable remote management and enable screen sharing.
Good luck!