The core difference: links vs answers
Classic SEO competes for a position in a list of ten blue links. The searcher still clicks through and decides for themselves. AI search competes to be the source the model names inside a single written answer, often before the user visits any site at all. One is about ranking a page; the other is about being quoted.
That changes the unit of work. For SEO you optimise a page for a keyword. For AI search you optimise an answer for a prompt, and you reinforce the brand entity and third-party citations the model leans on when it decides who to trust.