There is possible to have different product name and description because these attributes have store_view scope. Please take a look at screenshot
To update product programmatically code should be something like:
$sku = 'sku1';
$storeId = 0;
$objectManager = \Magento\Framework\App\ObjectManager::getInstance();
$_product = $obj->create('\Magento\Catalog\Api\ProductRepositoryInterface')->get($sku,true, $storeId, true);
$_product->setShortDescription('short description');
$_product->setCustomAttribute("abc", 'abc');
$_product->save($_product);
But in that case product short_description attribute will be updated in all scopes.
How to update product in selected store_view scope?
$storeId = 0;
to$storeId = ...your store id here...;