Both.
Any GameStop, EB Games, Electronics Boutique, Funcoland, Babbages or Software Etc. (yes, some still exist!) has the same policy - you can get store credit for your trade-ins or cash for 20% less. And cash cannot be combined with trade-in promotions. They all operate under the same company, they all have the rules and practices and there is nothing different about any of them other than the signage.
Not all non-GameStop stores will be changing names, but most will to maximize the marketing that has been occurring post-August. The company is trying to create a brand. Some stores will remain the same due to proximity to another location. For instance, I know one area that has a Funcoland and a GameStop inside the same mall. The Funcoland will remain a Funcoland in name only, simply because it looks like there are two different video game retailer options for customers. There's another mall that has a GameStop and a Babbages, where the Babbages will not be changing names due to the same reason.