Category List (Archive) Page Template By Category

You can create a category template named category-foo.php this will be applied only to category with slug foo. You can thus create custom template for different categories.

Source – Codex page for Category template

Note –

If you want to do some minor changes such as show foo in a category-1 and bar on other, then It’d be good to have a single category.php and use is_category conditional tags.

Update –

You can use get_template_part( $slug, $name ) to use different loops for different categories –

<?php 
if (is_category('foo')) {
    get_template_part( 'cat', 'foo' );  // It'll load    cat-foo.php
} else (is_category('bar')) {
    get_template_part( 'cat', 'bar' );  //   cat-bar.php
} else { 
    //
}
?>