Three-no products refer to products with no production date, no quality certificate (or production license) and no name of the manufacturer.
Trademark refers to a brand or part of a brand that is registered by the relevant government departments in accordance with the law and is called a "trademark". Trademarks are protected by law, and the registrant has exclusive rights.
Having a trademark does not necessarily mean that it is a three-no product, and not having a trademark does not necessarily mean that it is a three-no product. The specific situation needs to be determined