Because the naming convention is matter. You can create a new template for your different page and name it “page.php” and on the header portion give it a name:
<?php
/**
* Template name: Different page tempate
*/
get_header(); ?>
<div class="yourclass">
<!-- Your different template code should go here -->
</div>
<?php
get_footer();
Once you are done then go to Pages>Add New & on the right sidebar you will see the new template name under “Template” dropdown. Select it as your new page template and publish.