Generative AI (Gen AI) refers to deep learning artificial intelligence models that can create content such as text, images, and code based on training data the models were provided (IBM, 2023). Gen AI emerged in wider public awareness when OpenAI released ChatGPT in November 2022.
You most likely encounter Gen AI through a chat interface, such as ChatGPT or Google AI or Copilot. Underneath these interfaces are the actual models that do the generative work.
AI is a general, umbrella term. There are various forms of AI, many of which have been used in organizations for some time.

Source: Amaratunga, 2023
Amaratunga, T. (2023). Understanding large language models: Learning their underlying concepts and technologies. Apress Media LLC. https://catalog.library.vanderbilt.edu/permalink/01VAN_INST/18gthl0/alma991044248537503276