As you said, one is the corporate trademark and the other is the corporate product trademark. It is recommended to use the trademark you used before as the product trademark, so that it will be recognized in the market, and then mark the corporate trademark on the product packaging when the product is shipped to the factory.

The above is just my personal opinion. World Standard Enterprise Consulting and Management Company specializes in trademark registration, patent applications and ISO international quality system certification. Please Hi me if you need anything!