Here's the Wikipedia definition:
Generative artificial intelligence (GenAI) is a subfield of artificial intelligence (AI) that uses generative models to generate text, images, videos, audio, software code or other forms of data.[1] These models learn the underlying patterns and structures of their training data, and use them to generate new data[2] in response to input, which often takes the form of natural language prompts.
What part of it says it is just chatbots? Notice that of says "other forms of data" there? That is because audio, video, and chatbots are the most common cases, not the only cases. Prompts are not even needed. You just have a bunch of data points forming a distribution, and you want a model that samples faithfully from that distribution.
I agree that the word "AI" and even "generative AI" is being used to basically describe big tech that pushes their products on people like OpenAI and Anthropic, but you gotta understand that relying on context is bound to create misunderstanding. Context doesn't travel along like words do.
Subservience to what? Having basic common sense and not being drowned by hate is not subservience.