Brand registry is the process of registering your brand with Amazon, and trademark is getting the full rights for a specific term or name that you have which allows you to restrict the usage, etc.
A trademark is legal protection for a brand name, logo, or slogan. It prevents others from using the same or similar mark in a way that could confuse customers. The brand registry includes legal documentation of the company. If our brand is registered we can protect our rights.
A brand registry basically protect your listing on Amazon and protect your brand from other seller and a trademark means you can protect your brand name, logo either its word mark or design mark. if you can get a trademark on your chosen logo or brand name then no one can use your logo or brand name.