Is there a WordPress equivalent to MediaWiki templates

Well there are two easy answers to this , one being an actual template and the other being more of a snippet.

You can use get_template_part to call an actual PHP template file, for instance if you have a file called my-text.php you could use:

get_template_part( 'my-text' );

Or if you just want to go the shortcode route and call a snippet in your editor you can do something like:

function footag_func() {
     $foo = 'Brown Cow'
     return $foo;
}
add_shortcode('footag', 'footag_func');
// then just use [footag]