I'd like to point out that the TRD and GR branding do coexist together in the Japanese market. However, they have different roles.
GR branding is a factory trim level typically, as Veloist indicated above. The TRD branding, on the other hand, is exclusively for the aftermarket. TRD is more like a factory aftermarket brand in Japan.
A perfect example of this is the TRD aftermarket kit for the GR Yaris, which is obviously a GR branded product:
However, it is important to note that the TRD brand has become more synonymous with off-roading in the US, so I am not sure how the brand will be used in North America going forward.
Another example of a factory aftermarket brand by Toyota is Modellista. I don't imagine a Modellista kit will come out for the GR Corolla because it is more viewed as a luxury, VIP-style kit.