Difference between these 2 get category products call?

Question

I have 2 sets of codes to get products in category.

Set 1

$category = Mage::getModel('catalog/category')->load(4);
$products = Mage::getModel('catalog/product')
    ->getCollection()
    ->addCategoryFilter($category)
    ->load();

Set 2

$products = Mage::getModel('catalog/category')->load(4)
     ->getProductCollection()
     ->addAttributeToSelect('*') // add all attributes - optional
     ->addAttributeToFilter('status', 1) // enabled
     ->addAttributeToFilter('visibility', 4) //visibility in catalog,search
     ->setOrder('price', 'ASC'); //sets the order by price

With Set 1, I can obtain correct number of products (9 items in total), while in Set 2, I can only obtain 4 items (strange).

However, only Set 2 returns product model (and I can obtain information such as names from it). Set 1 returns the following object:

Mage_Catalog_Model_Product::__set_state(array(
   '_cacheTag' => 'catalog_product',
   '_eventPrefix' => 'catalog_product',
   '_eventObject' => 'product',
   '_canAffectOptions' => false,
   '_typeInstance' => NULL,
   '_typeInstanceSingleton' => NULL,
   '_linkInstance' => NULL,
   '_customOptions' => 
  array (
  ),
   '_urlModel' => NULL,
   '_errors' => 
  array (
  ),
   '_optionInstance' => NULL,
   '_options' => 
  array (
  ),
   '_reservedAttributes' => NULL,
   '_isDuplicable' => true,
   '_calculatePrice' => true,
   '_defaultValues' => 
  array (
  ),
   '_storeValuesFlags' => 
  array (
  ),
   '_lockedAttributes' => 
  array (
  ),
   '_isDeleteable' => true,
   '_isReadonly' => false,
   '_resourceName' => 'catalog/product',
   '_resource' => NULL,
   '_resourceCollectionName' => 'catalog/product_collection',
   '_dataSaveAllowed' => true,
   '_isObjectNew' => NULL,
   '_data' => 
  array (
    'entity_id' => '9',
    'entity_type_id' => '4',
    'attribute_set_id' => '4',
    'type_id' => 'simple',
    'sku' => 'SKU101',
    'has_options' => '0',
    'required_options' => '0',
    'created_at' => '2015-01-19 10:29:08',
    'updated_at' => '2015-07-20 08:09:53',
    'cat_index_position' => '1',
    'is_salable' => '1',
    'stock_item' => 
    Varien_Object::__set_state(array(
       '_data' => 
      array (
        'is_in_stock' => '1',
      ),
       '_hasDataChanges' => false,
       '_origData' => NULL,
       '_idFieldName' => NULL,
       '_isDeleted' => false,
       '_oldFieldsMap' => 
      array (
      ),
       '_syncFieldsMap' => 
      array (
      ),
    )),
  ),
   '_hasDataChanges' => true,
   '_origData' => NULL,
   '_idFieldName' => 'entity_id',
   '_isDeleted' => false,
   '_oldFieldsMap' => 
  array (
  ),
   '_syncFieldsMap' => 
  array (
  ),
))

How can I:

1. Get all products from Set 2? or
2. Get product name & URL from Set 1?

p.s. all items have:

• Status = Enable
• Visibility = Catalog, Search
• Price > 0
• Have stock left

Answer 1

Set 1, retrieves all products assigned to the category even if they are disabled or they not visible.
but you don't get the name or description because you don't have the ->addAttributeToSelect('*') set in the collection. Add the line right after getCollection().

In addition you can specify this also to the collection

->addUrlRewrite($category->getId())

to get the correct urls including the category path.

To get all products from set 2, you need to remove the filter on the status and visibility.