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.

AMIMOTO

horike

wokamoto

Kazuto Takeshita

webnist

gatespace

*Related posts based on categories, tags. 
*Can be replaced and sort of related posts at admin screen. 
*I can be added as an add-on another related posts algorithm.
You can make addon to use <a href="https://github.com/horike37/wp-simple-related-posts-addon-template/" rel="nofollow ugc">Addon Template</a>.
You can use JSON REST API Endpoint. Require plugin <a href="https://wordpress.org/plugins/json-rest-api/" rel="ugc">JSON REST API</a> 
 http://example.com/wp-json/posts/%post_id%/sirp_related/ 
 http://example.com/wp-json/sirp_related/%post_id%/ 
 http://example.com/wp-json/sirp_related/%post_id%/?filter[num]=5
<h4>Translators</h4>
<ul>
<li>Japanese(ja) – <a href="https://profiles.wordpress.org/horike" rel="nofollow ugc">Horike Takahiro</a></li>
<li>Thai(th_TH) – <a href="http://www.xn--12cg1cxchd0a2gzc1c5d5a.com" rel="nofollow ugc">TG Knowledge</a></li>
</ul>
<h4>Contributors</h4>
<ul>
<li>@<a href="https://profiles.wordpress.org/shinichin" rel="nofollow ugc">ShinichiN</a></li>
<li>@<a href="https://profiles.wordpress.org/webnist" rel="nofollow ugc">Webnist</a></li>
<li>@<a href="https://profiles.wordpress.org/mt8biz" rel="nofollow ugc">mt8biz</a></li>
</ul>

WP Simple Related Posts

Related Posts plugin. It's flexible and fast and simple.

Similarity vs WP Simple Related Posts