How to get Category Collection per Store in Magento 2?

Use directly objectmanager is not best/Recommended way to do in magento use Block with consturct and fetch method in your phtml file.

$categoryFactory = $objectManager->create('Magento\Catalog\Helper\Category');
$categoryFactory->getStoreCategories(false,false,true);

For More details kindly refer blogs link, Category Collection per store wise

Using Block way,

class Categorydata extends \Magento\Framework\View\Element\Template {
    protected $_categoryHelper;
    protected $categoryFactory;
    protected $_catalogLayer;

    public function __construct(
        \Magento\Catalog\Block\Product\Context $context,     
        \Magento\Catalog\Helper\Category $categoryHelper,        
        array $data = []
    ) {
        $this->_categoryHelper = $categoryHelper;   
        parent::__construct(
            $context,          
            $data
        );
    }

    /**
     * Retrieve current store level 2 category
     *
     * @param bool|string $sorted (if true display collection sorted as name otherwise sorted as based on id asc)
     * @param bool $asCollection (if true display all category otherwise display second level category menu visible category for current store)
     * @param bool $toLoad
     */

    public function getStoreCategories($sorted = false, $asCollection = false, $toLoad = true)
    {
        return $this->_categoryHelper->getStoreCategories($sorted , $asCollection, $toLoad);
    }

  }

call inside phtml file,

 $categorys = $this->getStoreCategories(false,false,true);
  foreach($categorys as $category){
     echo $category->getName()
  }

Create Block and add below code to your block.

namespace <vendor>\<module>\Block;

class FeaturedCategories extends \Magento\Framework\View\Element\Template{
protected $_categoryCollection;
protected $_storeManager;

public function __construct(
    \Magento\Backend\Block\Template\Context $context,
    \Magento\Store\Model\StoreManagerInterface $storeManager,
    \Magento\Catalog\Model\ResourceModel\Category\CollectionFactory $categoryCollection,
    array $data = []
)
{
    $this->_categoryCollection = $categoryCollection;
    $this->_storeManager = $storeManager;
    parent::__construct($context, $data);
}

public function getCategoryCollection()
{
    $collection = $this->_categoryCollection->create()
        ->addAttributeToSelect('*')
        ->setStore($this->_storeManager->getStore())
        //->addAttributeToFilter('attribute_code', '1')
        ->addAttributeToFilter('is_active','1');
   return $collection;
}
}

And $block->getCategoryCollection() used this in your template file. to get category collection

Try this :

protected $_storeManager;

public function __construct(
    \Magento\Store\Model\StoreManagerInterface $storeManager,
    $data = []
) {
    $this->_storeManager = $storeManager;
    parent::__construct($data);
}

$objectManager = $objectManager = \Magento\Framework\App\ObjectManager::getInstance();
$categoryFactory = $objectManager->create('Magento\Catalog\Model\ResourceModel\Category\CollectionFactory');
$categories = $categoryFactory->create()                              
    ->addAttributeToSelect('*')
    ->setStore($this->_storeManager->getStore()); //categories from current store will be fetched

foreach ($categories as $category){
    $category->getName();
}