To update cms static block for particular store programmatically you can use following code.
$objectManager = \Magento\Framework\App\ObjectManager::getInstance();
$identifier = 'block_identifier';
$store_id = 2;
try {
$block = $objectManager->create('Magento\Cms\Model\Block');
$block->setStoreId($store_id); // store for block you want to update
$block->load($identifier, 'identifier');
$block->setIdentifier($identifier);
$block->setTitle('Block Title');
$block->setIsActive(1);
$block->setStores($store_id);
$block->setContent($content);
$block->save();
echo "Static block updated! \n";
} catch (Exception $e) {
echo $e->getMessage();
}