GAN's are simply a a framework providing a technique for adversarial training of generative models. In fact the discriminator essentially is a supervised learning paradigm unless we use a more complicated architecture like introduced in the SeqGAN model where the discriminator goes through a policy gradient loop and the reward helps decide on the generated outputs probability. Similarly the generator architecture could involve anything from a simple supervised MLP or con nets like in DCGan or seq2seq lstms depending on whatever type of data one was generating.