Haha, I'm happy to go deep on this if you want, but will keep this post shortish.

Types of data (structured vs unstructured) and types of ML (supervised vs unsupervised vs reinforcement learning) are different.

The way Generative AI models are trained is generally very different than genetic algorithms and typically uses a mixture of Reinforcement Learning and Supervised learning with a diffusion or transformer backend (type of deep learning layer).

GANs probably count as generative AI, but predate the current AI models by a few years. Their approach is more about competing models than survival of the fittest, as it has a model that generates and a model that critiques. Their main drawback was that they could really only output content in a narrow range (faces or landscapes, but not both).