How to display two blog categories as separate sections on one page?

To achieve this I would recommend using the WP_Query class.

When using this approach, you are able to specify the parameters to search for posts (or categories) by.

For your particular question you should look at the Category Parameters. To target the categories you are looking for, you could do so by using their ID or their slug with the appropriate parameter label.

For example:

// WP_Query arguments
$args = array(
    'category_name'          => 'category-1',
);

// The Query
$query = new WP_Query( $args );

// The Loop
if ( $query->have_posts() ) {
    while ( $query->have_posts() ) {
        $query->the_post();
        // do something
    }
} else {
    // no posts found
}

In the section where ‘// do something” appears, is where you define what should be printed to the page.

There are useful websites you can use that generate this code for you – one such is GenerateWP.