"Generative AI" isn't just an adjective applied to a noun, it's a specific marketing term that's used as the collective category for language models and image/video model -- things which "generate" content.
What I assume you mean is "I think <term> is misleading, and would prefer to make a distinction".
But how you actually phrased it reads as "<term> doesn't mean <accepted definition of the term>, but rather <definition I made up which contains only the subset of the original definition I dislike>. What you mean is <term made up on the spot to distinguish the 'good' subset of the accepted definition>"
I see this all the time in politics, and it muddies the discussion so much because you can't have a coherent conversation. (And AI is very much a political topic these days.) It's the illusion of nuance -- which actually just serves as an excuse to avoid engaging with the nuance that actually exists in the real category. (Research AI is generative AI; they are not cleanly separable categories which you can define without artificial/external distinctions.)