tagsmetabox_like_categoriesmetabox.php

<?php
function kuaf_post_tags_meta_box_remove() {
	$id = 'tagsdiv-post_tag'; // you can find it in a page source code (Ctrl+U)
	$post_type = 'post'; // remove only from post edit screen
	$position = 'side';
	remove_meta_box( $id, $post_type, $position );
}
add_action( 'admin_menu', 'kuaf_post_tags_meta_box_remove');

function kuaf_add_new_tags_metabox(){
	$id = 'kuaftagsdiv-post_tag'; // it should be unique
	$heading = 'Tags'; // meta box heading
	$callback = 'kuaf_metabox_content'; // the name of the callback function
	$post_type = 'post';
	$position = 'side';
	$pri = 'default'; // priority, 'default' is good for us
	add_meta_box( $id, $heading, $callback, $post_type, $position, $pri );
}
add_action( 'admin_menu', 'kuaf_add_new_tags_metabox');

function kuaf_metabox_content($post) {  
 
	// get all blog post tags as an array of objects
	$all_tags = get_terms( array('taxonomy' => 'post_tag', 'hide_empty' => 0) ); 
 
	// get all tags assigned to a post
	$all_tags_of_post = get_the_terms( $post->ID, 'post_tag' );  
 
	// create an array of post tags ids
	$ids = array();
	if ( $all_tags_of_post ) {
		foreach ($all_tags_of_post as $tag ) {
			$ids[] = $tag->term_id;
		}
	}
 
	// HTML
	echo '<div id="taxonomy-post_tag" class="categorydiv">';
	echo '<input type="hidden" name="tax_input[post_tag][]" value="0" />';
	echo '<ul>';
	foreach( $all_tags as $tag ){
		// unchecked by default
		$checked = "";
		// if an ID of a tag in the loop is in the array of assigned post tags - then check the checkbox
		if ( in_array( $tag->term_id, $ids ) ) {
			$checked = " checked='checked'";
		}
		$id = 'post_tag-' . $tag->term_id;
		echo "<li id='{$id}'>";
		echo "<label><input type='checkbox' name='tax_input[post_tag][]' id='in-$id'". $checked ." value='$tag->slug' /> $tag->name</label><br />";
		echo "</li>";
	}
	echo '</ul></div>'; // end HTML
}
?>