Trademark right refers to the "right to use a trademark": producers or service providers have the right to use trademarks to distinguish them from other producers or service providers

Trademark Exclusive right refers to the "right to use an exclusive trademark": the trademark used by a producer or service provider is protected by law after registration application. It is its exclusive trademark. Other producers or service providers may not use it without its permission. Powers used

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A bit convoluted. The core difference between the two is "proprietary".