I want to display subcategories under artist category in one layout and design and other categories in another layout and design in Magento 1.4.1.1.
The best way to do this is to use static blocks.
1) Create phtml file in /template/catalog/navigation
<?php $_categories = $this->getCurrentChildCategories(); ?>
<ul>
<?php foreach ($_categories as $_category): ?>
<?php if($_category->getIsActive()): ?>
<li>
<a href="<?php echo $_category->getURL() ?>" title="<?php echo $this->htmlEscape($_category->getName()) ?>"><?php echo $this->htmlEscape($_category->getName()) ?></a>
</li>
<?php endif; ?>
<?php endforeach; ?>
</ul>
2) Create static block "Subcategories"
{{block type="catalog/navigation" template="catalog/navigation/subcategory.phtml"}}
3) Assign static block for needed category ("Display Settings" tab -> Display Mode = Static block only and select CMS Block "Subcategories")