Wordpress - Check if post is being published for the first time, or is an already published post being updated

Hook into edit_post to catch changes. And take a look at wp_transition_post_status() which is called on inserts and updates:

function wp_transition_post_status($new_status, $old_status, $post) {
    do_action('transition_post_status', $new_status, $old_status, $post);
    do_action("{$old_status}_to_{$new_status}", $post);
    do_action("{$new_status}_{$post->post_type}", $post->ID, $post);
}

On publish you hook into

• draft_to_publish,
• pending_to_publish and
• auto-draft_to_publish.

For edits hook into publish_to_publish.

Example

A mini plugin that notifies all authors during post publish or edit.

<?php
/**
 * Plugin Name: (#56779) Notify authors
 */
add_action( 'transition_post_status', 'wpse_56779_notify_authors', 10, 3 );
function wpse_56779_notify_authors( $new_status, $old_status, $post )
{
    if ( 'publish' !== $new_status )
        return;

    $subject = 'publish' === $old_status
        ? __( 'Edited: %s', 'your_textdomain' )
        : __( 'New post: %s', 'your_textdomain' );

    $authors = new WP_User_Query( array( 'role' => 'Author' ) );
    foreach ( $authors as $author )
    {
        wp_mail(
            $author->user_email,
            sprintf( $subject, $post->post_title ),
            $post->post_content
            // Headers
            // Attachments
        );
        // Slow down
        sleep( 5 );
    }
}