The recent explosion in artificial intelligence and its integration into more and more domains beyond traditional ones such as health care, insurance, and defence show no signs of slowing down. Generative AI is becoming part and parcel of an increasing number of designerly activities as either a tool—for example in the form of the Large Language Generative Models that enable the creation of text, images, videos, or mock-ups via chatbot-like interfaces—or a material—for example when creating the interfaces that others will use to interact with such models. Rapid adoption and low AI literacy among designers’ limits awareness of limitations, challenges, opportunities, and consequences deriving from the use of AI-enabled products and services. The paper introduces the concept of Design Literacy for AI as distinct from AI Literacy and Design Literacy, and proposes a design-centred taxonomy of Generative AI products and services. The taxonomy is operationalised into a proof-of-concept web service using faceted classification to help designers better understand AI as both a tool and a material, further investigate the concept of Design Literacy for AI, and contribute to reducing the gap between AI development and design practices.