Edit Posts Page but not category specific pages?

You can create a Page template in which display all posts with your custom markup.

<?php

/**
 * Template Name: My Custom Blog
 *
 */

// The Query
$args = array('posts_per_page'=>-1);
$the_query = new WP_Query( $args );

// The Loop
if ( $the_query->have_posts() ) {
    echo '<ul>';
    while ( $the_query->have_posts() ) {
        $the_query->the_post();
        echo '<li>' . get_the_title() . '</li>';
    }
    echo '</ul>';
} else {
    // no posts found
}
/* Restore original Post Data */
wp_reset_postdata();

?>

Name this page as: “page-custom_blog.php”
After, just publish a new page assigning this template.

Hope it helps.

https://developer.wordpress.org/themes/template-files-section/page-template-files/page-templates/