Unity object cloning and public/private variables

I've noticed that when cloning objects in Unity, the values of public variables are carried over, but private variables are not. I'd like to know the exact rules around this because I can't find it in the documentation or the forums. Might be to do with serialization of public variables?

Example, say we have a simple GameObject with the following script:

 using UnityEngine;
 
 public class TestObjScript : MonoBehaviour {
     public bool HaveInited = false;
 
     public void Init() {
         if (HaveInited) {
             print("Skipping Init");
             return;
         }
         print("Init");
         HaveInited = true;
     }
 }

And then we make an object cloner:

 public class TestObjCloner : MonoBehaviour {
 
     public TestObjScript Original;
     TestObjScript origInstance;
 
     // Use this for initialization
     void Awake () {
         origInstance = (TestObjScript)Instantiate(Original);
         origInstance.Init();
         for (int i = 0; i < 2; i++) {
             TestObjScript newObj = (TestObjScript)Instantiate(origInstance);
             newObj.Init();
         }
     }
 }

Output is:

• Init

• Skipping Init

• Skipping Init

But say we make HaveInited a private variable; then output is:

• Init

• Init

• Init