Magento: Product collection filter by category Id

in Cms Page

Go to “CMS – Manage Pages” and select “Home Page” from the list of pages.
Use this code snippet to show one category on your front page:

{{block type="catalog/product_list" name="home.catalog.product.list" alias="products_homepage" category_id="4" template="catalog/product/list.phtml"}}

For All Products

{{block type="catalog/product_list" name="home.catalog.product.list" alias="products_homepage" template="catalog/product/list.phtml"}}

in Phtml Page:

<?php
/**
* For current category
*/
$category = Mage::registry('current_category');
 
/**
* For a specific category
*/
$categoryId = 10;
$category = Mage::getModel('catalog/category')->load($categoryId);
 
/**
* Product collection for a particular category
*/
$productCollection = Mage::getResourceModel('catalog/product_collection')
                    ->addCategoryFilter($category)
                    ->addAttributeToSelect('*');
 
/**
* Filter result for only visible or status enable products
*/
Mage::getSingleton('catalog/product_status')
->addVisibleFilterToCollection($prodCollection);	
Mage::getSingleton('catalog/product_visibility')
->addVisibleInCatalogFilterToCollection($prodCollection);
 
/**
* Printing category and products name
*/
echo '<strong>'.$category->getName().'</strong><br />';
foreach ($prodCollection as $val) {
echo $val->getName() . '<br />';
}
?>