The terms are used interchangeably and they should not be.
Plain definitions
SEO is optimising to rank in a list of blue links. Measurable by position, well understood, decades of practice behind it.
AEO, answer engine optimisation, is making a page readable and quotable by a system that answers a question directly. It is deterministic. The crawler is allowed in or it is not. The schema carries a value or it does not. You can check it today, on your own site, with no external service.
GEO, generative engine optimisation, is about whether a generative model actually mentions your brand when someone asks. It is probabilistic. The same prompt returns different answers to different people at different times, so a single observation tells you almost nothing.
The measurement difference is the whole story
AEO answers a yes or no question about your own property. GEO answers a statistical question about someone else's system.
That difference matters more than the vocabulary. If a tool reports a single confident "visibility score" for GEO, ask how many observations it is built on and what the confidence interval is. A rate without a sample size is not a measurement.
Which one to act on first
AEO, without much argument. It is deterministic, it is entirely within your control, and it gates the other two. An engine that cannot fetch or parse your page cannot cite you no matter how good the content is.
Search Overflow audits the AEO half today: crawler access, rendering, and whether structured data carries real values. Live GEO measurement, sampling what engines actually say over time, is being built and is not part of the product yet. We would rather say that plainly than sell you a number we cannot stand behind.