If “machine learning” is taken to be so broad as to include any artificial neural network, all of which are trained with back propagation these days, then it is useless as a term.
The term “machine learning” was coined in the era of specialized classification agents that would learn how to segment inputs in some way. Thing email spam detection, or identifying cat pictures. These algorithms are still an essential part of both the pre-training and RLHF fine tuning of LLM models. But the generative architectures are new and very essential to the current interest in and hype surrounding AI at this point in time.
From where I sit, the generative models provide more flexibility but tend to underperform on any particular task relative to a targeted machine learning effort, once you actually do the work on comparative evaluation.
You appear to be comparing apples to oranges. A generation task is not a categorization task. Machine learning solves categorization problems. Generative AI uses model trained by machine learning methods, but in a very different architecture to solve generative problems. Completely different and incomparable application domain.