David Miller

Similarity displays a list of posts similar to the current post with similarity being determined based on tags, categories, or both. The display of the list is fully customizable including the ability to display the strength of the similarity as a value, percentage, color, or custom text/code. Another option allows for a less related post to be randomly selected and appended to the list. The list can be limited by one or both of a numerical limit or (as of version 2.1) match strength.
This plugin is translation ready and comes with English (U.S.), French, Polish, German, italian, and Spanish translations. Thanks to Li-An (http://li-an.fr/blog/) for providing the French translation. Thanks to Krzysztof Kudlacik (http://born66.net/) for providing the Polish translation. Thanks to Bjoern Buerstinghaus (http://www.buerstinghaus.net/) for providing the German, Italian and Spanish translations.
Prior to Version 1.6 private posts would potentially show in the list of related posts. In 1.6 these were skipped. As of version 1.7 private posts will show for the post author or others with the ability to read private posts. It is strongly recommended that users who have private posts install version 1.6 or higher.
The plugin allows for three function calls anywhere in your page templates (all use the same options):
<ul>
<li><code><?php sim_by_tag(); ?></code> – determines similarity based on the tags applied to the posts</li>
<li><code><?php sim_by_cat(); ?></code> – determines similarity based on the categories assigned to the posts</li>
<li><code><?php sim_by_mix(); ?></code> – determines similarity based on the tags and categories assigned to the posts</li>
</ul>
There are also three function calls that are better suited for use in sidebars (specifically when the sidebar is used on the main page)
<ul>
<li><code><?php sim_by_tag_multi(); ?></code> – determines similarity based on the tags applied to the first post on milti-post pages</li>
<li><code><?php sim_by_cat_multi(); ?></code> – determines similarity based on the categories assigned to the first post on milti-post pages</li>
<li><code><?php sim_by_mix(_multi); ?></code> – determines similarity based on the categories and tags assigned to the first post on milti-post pages weighting each according to the ratio you assign</li>
<li>To display a Similarity list as a widget use a text widget with one of the following shortcodes – <code>[SIM-BY-TAG]</code> <code>[SIM-BY-CAT]</code> <code>[SIM-BY-MIX]</code> for single post pages only or for all pages use <code>[SIM-BY-TAG-MULTI]</code> <code>[SIM-BY-CAT-MULTI]</code> or <code>[SIM-BY-MIX-MULTI]</code></li>
<li>To display a Similarity list without altering your templates simply select the function that you would like to auto-display at the bottom of the options page.</li>
</ul>

Similarity

Similarity displays a list of posts similar to the current post with similarity being determined based on tags, categories, or both.

keesiemeijer

Quickly increase your readers’ engagement by adding related posts in the sidebar or after post content with a widget or shortcode.
Posts with the most terms in common will display at the top!
This plugin is capable of finding related posts in multiple taxonomies and post types. Include or exclude terms from the search for related posts. Change the look and feel by using your own templates in a (child) theme.
<a href="http://keesiemeijer.wordpress.com/related-posts-by-taxonomy/" rel="nofollow ugc">plugin documentation</a>
Plugin features:
<ul>
<li>Widget and Shortcode.</li>
<li>Display related posts as post thumbnails, links, excerpts or full posts.</li>
<li>Small Footprint. Doesn’t slow down your site!</li>
<li>Automatic display of related posts after the post content.</li>
<li>Exclude or include terms and posts.</li>
<li>Search for related posts in single or multiple taxonomies and post types.</li>
<li>Limit the search for related posts by date, number or post meta.</li>
<li>Use your own HTML templates for display of the related posts.</li>
<li>Extensive <a href="http://keesiemeijer.wordpress.com/related-posts-by-taxonomy/" rel="nofollow ugc">plugin documentation</a>.</li>
<li>Follows WordPress coding standards and plugin best practices.</li>
<li>Highly Adjustable!</li>
</ul>
For the following features you need to be somewhat familiar with WordPress <a href="https://developer.wordpress.org/plugins/hooks/" rel="nofollow ugc">hooks</a>. The <a href="http://keesiemeijer.wordpress.com/related-posts-by-taxonomy/" rel="nofollow ugc">plugin documentation</a> has many examples to help you along.
Extended features:
<ul>
<li>Use a persistent cache for the related posts query. (opt-in feature)</li>
<li>Use the WordPress REST API to get related posts. (opt-in feature)</li>
<li>Load related posts after the whole page has loaded (with Ajax). (opt-in feature)</li>
<li>Use plugin functions in your theme templates to display related posts yourself.</li>
<li>Use Filters to change the default behavior of the plugin. </li>
</ul>
Follow this plugin on <a href="https://github.com/keesiemeijer/related-posts-by-taxonomy" rel="nofollow ugc">GitHub</a>. 
Search the <a href="https://keesiemeijer.github.io/related-posts-by-taxonomy" rel="nofollow ugc">code reference</a>
See the <a href="https://wordpress.org/extend/plugins/related-posts-by-taxonomy/faq/" rel="ugc">FAQ</a> to have related posts automatically display after the post content without using the shortcode or widget.
Default usage for the shortcode is:
<pre><code>[related_posts_by_tax]
</code></pre>
Attributes for the shortcode are:
<ul>
<li><code>post_id</code></li>
<li><code>taxonomies</code></li>
<li><code>post_types</code></li>
<li><code>posts_per_page</code></li>
<li><code>order</code></li>
<li><code>orderby</code></li>
<li><code>before_shortcode</code></li>
<li><code>after_shortcode</code></li>
<li><code>title</code></li>
<li><code>show_date</code></li>
<li><code>before_title</code></li>
<li><code>after_title</code></li>
<li><code>include_terms</code></li>
<li><code>include_parents</code></li>
<li><code>include_children</code></li>
<li><code>exclude_terms</code></li>
<li><code>exclude_posts</code></li>
<li><code>format</code></li>
<li><code>gallery_format</code></li>
<li><code>image_size</code></li>
<li><code>columns</code></li>
<li><code>caption</code></li>
<li><code>link_caption</code></li>
<li><code>limit_posts</code></li>
<li><code>limit_month</code></li>
<li><code>meta_key</code></li>
<li><code>meta_value</code></li>
<li><code>meta_compare</code></li>
<li><code>meta_type</code></li>
<li><code>public_only</code></li>
<li><code>include_self</code></li>
<li><code>post_class</code></li>
</ul>
Example to show 10 related posts instead of the default 5.
<pre><code>[related_posts_by_tax posts_per_page="10"]
</code></pre>
See the <a href="https://keesiemeijer.wordpress.com/related-posts-by-taxonomy/#shortcode" rel="nofollow ugc">documentation</a> for more information about these attributes.
<h4>Translations</h4>
<ul>
<li>Dutch </li>
<li>French (by <a href="http://www.artisanathai.fr" rel="nofollow ugc">Annie Stasse</a>) </li>
<li>Spanish (by <a href="http://www.ludobooks.com" rel="nofollow ugc">Ludobooks – Cuentos personalizados</a>) </li>
<li>Catalan (by <a href="http://www.ludobooks.com" rel="nofollow ugc">Ludobooks – Cuentos personalizados</a>) </li>
<li>Polish (by <a href="http://rekolekcje.net.pl" rel="nofollow ugc">koda0601</a>)</li>
</ul>

My goodness!

Display a list of related posts on your site based on the most terms in common. Supports thumbnails, shortcodes, a widget and more.

Similarity vs Related Posts by Taxonomy