Out of the box, Site Studio nodeIds are unique across all websites on a WebCenter Content instance. However, there is a configuration flag to change this. If the WebCenter Content configuration flag SSGenerateUniqueNodeIds is set to 0 (false), nodeIds will only be unique within each website.
Be careful changing the default value for SSGenerateUniqueNodeIds to be false. It is usually assumed that nodeIds are unique across all websites on a server and many times this is the way the code has been written.