Echo Text If User Is Logged in But NOT the Author of post

Try something like this in your template tags (or wherever in your theme):

function should_display_link() {
    $post = get_post();

    // Something went wrong, bail. (You should always have a post, in theory)
    if ( ! $post ) {
        return false;
    }

    $current_user = get_current_user_id();

    // Assuming only logged-in users can subscribe.
    if ( ! $current_user ) {
        return false;
    }

    return absint( $post->post_author ) !== absint( $current_user );
}

In your template, you can use it like this:

<?php if ( should_display_link() ) : ?>
    <!-- Your link code here -->
<?php endif; ?>