What's the difference between global var post and get_post?

I use the_posts filter to add an object to each queried post. When access the added object, I get different result by using $post or get_post.
This is the code to attach the object to posts:

add_filter( 'the_posts', 'populate_posts_obj', 10,2 );
function populate_posts_obj( $posts, $query ){
  if ( !count( $posts ) ||  !isset($query->query['post_type']) )
    return $posts;
  if( in_array( $query->query['post_type'], get_valid_grade_types())){
      foreach ( $posts as $post ) {
         if (  $obj = new Gradebook( $post->ID ) )
            $post->gradebook = $obj;
      }
   }
  return $posts;
}

Then, access the obj via $post, sometimes get the obj, sometimes not (even when it's the same post):

function get_the_gradebook(){
  global $post;
  return isset($post->gradebook) ? $post->gradebook : null;
}

Access the obj via get_post(), always get the obj:

function get_the_gradebook(){
global $post;
  $p = get_post($post->ID);
  return isset($p->gradebook) ? $p->gradebook : null;
}

I can just use the get_post() version, but it would be useful if I know why the difference.

Additional info:

If you ask the reason I attach an obj to each post, I think WordPress may take care of the caching process at the first place. Then, other caching plugins can work on my obj as if working on standard WP posts.

Solution

Lets explain you with a little bit pseudo code. I am trying to be broad with my approach so that my answer is relevant to StackOverflow however I still don't know how many down votes I may be receiving for this.

The simple difference is $post is a variable and get_post() is a method that means you can expect a different output from get_post() due to several dependencies however $post will only change when you explicitly do that.

Lets assume something like this

function get_post() {
    return rand(0, 5);
}

$post = get_post(); /* lets assume random 
                       value that was generated 
                       this time was "2" */

Now each time you call get_post() its value be keep changing however the value of $post is always 2.

Coming back to the context of wordpress, $post is set using get_post() within the Loop and corresponds to the object referring to default post ID for current URL where as get_post() will take post ID as an input and return the post object.