Is there a different login system to the database and to the forums? When I try to retrieve data, it returns a message: 

The query will return 28011 records.
It's not recommended to view it on screen (1000 records limit).
Please modify your query (or select additional selection from below) or click download (not applicable for guest user).

The system classifies me as a guest user and I'm not able to login with the same password as to the forums.

Thank you.

Yes. Database and Forum are managed by two different login systems. Forum is opened to everybody but, in database, advanced features (such as download option, saving queries, creating commodity/country groups) reserved for subscribers.

By default, all database users will be authenticated as "Guest User" that can view on-screen but no download option.

As an alternative, you can access part of UN Comtrade data via UNdata (data.un.org), there you will be able to download up to 50,000 records per query.