Network - Change Varible Across Clients

Hello,

I have a script in my scene that controls the scoring of my game. There is only one instance of this script, and new one IS NOT instantiated when a new player joins.

So there is always one. My question is, if the server makes a change to a variable on this script, will all the clients receive these changes too? Automatically?

So for example, there is a variable called overallScore, in which the server controls. If the server changes this value to 10, will this value change to 10 on the client scripts too?

My understanding is that, if you have one of something in the scene (this script in this case), and a client joins, you technically now have 2 instance of that script and so you need to sync the two together. Correct?

Example:

 if(Network.isServer){
    overallScore = 10;
 }

This will only change the overallScore on the server side to 10, right? Whereas:

 if(Network.isServer){
    networkView.RPC("ChangeScore", RPCMode.All, 10);
 }
 
 @RPC
 function ChangeScore(new : int){
    overallScore = new;
 }

This will be called only by the server, but apply the changes to the clients too. Right?

Do I have to do this all the time? What if I just want to share all the variables on this script, so its the 'centre' of the game?