Custom Post Type Category On Admin

You’ve added the following line to arguments: 'taxonomies' => array( 'category', 'post_tag' ),. It will register the same categories and tags to video post type which you’re using with default posts.

First things first: remove line 'taxonomies' => array( 'category', 'post_tag' ),

In order to have a new “exclusive” taxonomy only for video post type, you’ll need to register a new taxonomy. This should go to same .php file where you’re registering your new post type if it’s exclusive to only video post type. This is not mandatory but it’s better for future maintenance.

I’ve added few arguments that I usually specify. See all the possible args here. Read the whole document to get what you actually need. Some of these arguments alter the behaviour a lot.

// Video categories
add_action( 'init', 'register_taxonomy_video_category', 0 );

function register_taxonomy_video_category() {

    $labels = array(
        // See list of labels in docs I linked above (bold and blue "here")     
    );


    $args = array(  

        // Custom labels? Remove them all to get "default"
        'labels'              => $labels,
        // Does these have child-parent relationships?
        'hierarchical'        => true,
        // Translatable pretty slugs?
        'rewrite'             => array( 'slug' => __( 'video-category', 'video' ) ),
        // Generate a default UI for managing this taxonomy?
        'show_ui'             => true,
        // Allow automatic creation of taxonomy columns on associated post-types table?
        'show_admin_column'   => true,
        // Show in quick edit panel?
        'show_in_quick_edit'  => false
        )  
    );

    // "video-category" is the name of the taxonomy
    // "video" is the post type you want it to use with
    register_taxonomy( 'video-category', 'video', $args );
}