Generative engine optimisation (GEO, also spelled optimization), which some agencies call AI SEO, is the work of getting your brand named and cited in AI-generated answers: ChatGPT, Google AI Overviews and AI Mode, Perplexity, Gemini and Claude.
Every engine builds an answer the same way. It reads the prompt, searches an index of the web, keeps the sources that agree with each other, then writes an answer naming the brands those sources support. GEO works on the middle two steps: being in the index, and being the brand the sources agree on.
Answer engine optimisation (AEO) is the older, narrower idea of shaping a page so a search engine lifts it as the direct answer. GEO includes that, and adds everything off your site that AI checks before it names you.