How to update the 'modified_time' of a post ONLY when content is changed?

I have modified @s_ha_dum's answer a bit to better suit my needs. If post has less than 30 chars added to the content, in that case the time won't be changed.

add_action('wp_insert_post_data', 'post_content_check_wpse_135268', 10, 2);
function post_content_check_wpse_135268($data, $postarr) {

    if (empty($postarr['ID'])) 
        return $data;

    $old = get_post($postarr['ID']);
    $old_content_length = strlen($old->post_content);
    $new_content_length = strlen($data['post_content']);

    // Calculate length between old and new content
    $length_difference = abs($old_content_length - $new_content_length);

    // If new content has less than 30 new characters then set modified time to previous time
    if (!empty($old) && $length_difference < 30) {

        $data['post_modified'] = $old->post_modified;
        $data['post_modified_gmt'] = $old->post_modified_gmt;

    }

    return $data;

}

Crude and minimally tested but...

function post_content_check_wpse_135268($data,$postarr){
  if (empty($postarr['ID'])) return $data;
  $old = get_post($postarr['ID']);
  if (!empty($old) && ($old->post_content === $data['post_content'])) {
    $data['post_modified'] = $old->post_modified;
    $data['post_modified_gmt'] = $old->post_modified_gmt;
  }
  return $data;
}
add_action('wp_insert_post_data','post_content_check_wpse_135268',10,2);

The code compares the existing post content in the database to the new post content. If they are the same the old modified date information is used. That should mean that the date gets changed only if the post content is changed.

The comparison is very crude-- a simple ===. You probably want something more complex-- for example, something that will ignore spurious whitespace.

I guess, there is no exact way of retrieving the time only when the post's content is updated until you change the core functionality of wordpress and that might lead to some other issues. But here is a workaround I would like to propose here.

You can retrieve the time/date only when content is updated via revisions. A revision is created only when you change the content of the post, not otherwise.

But there is no exact way of retrieving only date/time but a set of parameters.

Use this code and it'll give you a string that contains the required data:

<?php 
    echo wp_post_revision_title_expanded($post,false);
?>

What you can do now is fetch the complete string in a variable and use regular expression to extract the desired stuff.

Reference: Codex link. Nut nothing much is available here.

EDIT: (thanx for the function update)

This is the code based on wp_post_revision_title() and working as expected.

<?php
    $revision_data = wp_post_revision_title( $post ,false );
    $date_time = explode('@', explode('[', $revision_data)[0]);
    echo '<p>Date:'.$date_time[0].'</p>';
    echo '<p>Time:'.$date_time[1].'</p>';
?>