same blog on both websites

If the two domains are hosted on the same server – you probably, made the mistake of NOT using a new, different table prefix for the second blog. I suspect they are both in the same database, in which case you should change in one of the wp-config.php file this line:
$table_prefix = 'wp_'; // Only numbers, letters, and underscores please!

You should replace the wp_ part with something else, like:
wp2_
blog_
ms_
whatever_

Save and re-upload the file.
Run the installation script for this blog again.
You should be fine after that.