Input.GetMouseButtonDown(0) will return true whenever mouse button
0 is pressed, no matter if the mouse is only pressed over the object that has that code in it's script.
You might be thinking, instead of
Update to use
OnMouseDown(), which only activates when that object's collider is clicked. But, you'd still being using Unity's buttons wrong.
What you need to do is a create a public
SceneChange method, doesn't even have to be in a script attached to your button, just somewhere in the scene, perhaps on a
GameManager object. Then is that
OnClick event that's in your Button properties:
Runtime where it currently says
Button, select the object that's holding the script with your
SceneChange method. Then the drop down to the right will populate with a list of scripts, and sublists of their public methods. Select your
SceneChange method from that drop down.
Now when your button is clicked, it'll fire an event which will trigger your
SceneChange method, and it'll only be from the button you choose.
See this tutorial from Unity for a walkthrough of how to create these methods.