I presume when they say "AI is used for data analysis" they're talking about traditional AI (more frequently referred to as "machine learning") rather than generative AI (LLMs).
Traditional AI isn't "referred to" as Machine Learning, they're separate things. ML is a subset of the field of AI, that focuses on AI algorithms that (loosely speaking) "learn" from data, as opposed to being AI that is explicitly defined.
And LLMs belong to this subset. They're largely built using supervised machine learning.
But also, "AI" is polysemous. There's "AI" the academic field, and machine learning is a subset of that field. But there's also "AI" the marketing term, which is much more well-known nowadays. And for that meaning of the term, it's the other way around -- it's a subset of machine learning.
Under either definition, though, I agree it doesn't make much sense to talk about them as if they are two different things, because either way one is just a particular kind of the other.