How can I get content inside one shortcode to another shortcode?

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There is no definitive way of doing that in WordPress, but here are some options for you:

  1. Use a global variable to store the reference list, i.e. the content as in [ref]content here[/ref]. But I personally don’t recommend and wouldn’t be using global variable.

  2. Use a custom PHP class and add the shortcode functions as methods in that class, then use a property (e.g. private $ref_list = [];) to store the reference list. So for example inside the ref_shortcode() method, you could do $this->ref_list[] = $content;.

  3. Use the object caching API in WordPress, e.g. use wp_cache_set() to store the reference list.

And I’m not asking you to use the third option above, but since your code originally not in a PHP class, then here’s a working example using the object caching API:

function ref_shortcode( $atts = array(), $content = null ) {
    if ( ! empty( $content ) ) {
        $post_id = get_the_ID();

        // Retrieve current list of references for the current post.
        $refs = wp_cache_get( "post_{$post_id}_references" );
        $refs = is_array( $refs ) ? $refs : array();

        // Then add the current reference to the list.
        $refs[] = $content;
        wp_cache_set( "post_{$post_id}_references", $refs );

        $j = count( $refs );
        return "<a href="#ref-$post_id-$j"><sup>[$j]</sup></a>";
    }

    return '';
}
add_shortcode( 'ref', 'ref_shortcode' );

function references_shortcode( $atts = array(), $content = null ) {
    $post_id = get_the_ID();
    $refs = (array) wp_cache_get( "post_{$post_id}_references" );
    $output="";

    if ( ! empty( $refs ) ) {
        $output="<h3>References</h3>";
        $output .= '<ul>';

        foreach ( $refs as $i => $ref ) {
            $j = $i + 1;
            $output .= "<li id='ref-$post_id-$j'>$ref</li>";
        }

        $output .= '</ul>';
    }

    return $output;
}
add_shortcode( 'references' , 'references_shortcode' );