Style post formats differently on the home page

Ok, your theme is already set up to use different post formats, so in your case you would just need to do the following:

Change the line in content-aside.php that reads

the_content('Weiterlesen');

To read

the_excerpt();

Change just that one line, save your changes, and it should work how you want.

• the_content() echos the post content
• the_excerpt() echos the excerpt

By changing the_content() to the_excerpt() in the content-aside.php file, you will make your aside posts just display the excerpt.

(removed the long explanation now that we can see what you have to work with)

Since it uses that loop on both, try the following instead

<article id="post-<?php the_ID(); ?>" <?php post_class();?> >
        <h1>
            <?php if(is_single()) {?>
            <?php the_title();?>
            <?php } else { ?>
            <a href="https://wordpress.stackexchange.com/questions/176525/<?php the_permalink();?>"><?php the_title();?></a>
            <?php }?>
        </h1>
        <div class="postMeta2">
            <a href="https://wordpress.stackexchange.com/questions/176525/<?php the_permalink();?>"><?php the_time('j. F Y') ; ?> </a>
        </div>
        <section class="multi-column">
            <?php
                if ( is_home() ) {
                    the_excerpt();
                } else {
                    the_content('Weiterlesen');
                }
            ?>
        </section>
        <div class="postInfo">
            <div class="postCategories">
                Bereich: <br> <?php the_category(', ') ?>
            </div>              
        </div>
    </article>

That should do the trick (just adds a check to only do the_excerpt() on the home page)