Besides changes in the architecture, different GAN variants use different loss functions, connections, inputs etc.
This older paper 1 gives a brief overview. You can also find some blog posts about different GANs, but I’m not sure if there is a good “complete” overview.
If I’m not mistaken, at one point a lot of new GAN architectures were published daily on arxiv, so it was quite hard to follow which variant might be promising.