Today we have cars. In 30 years we will have cars. But in the meantime, some cars will will driven by humans and others not, and there will be terms to distinguish them.
Today, most people use the terms Autonomous, Automated, Self-Driving, and Driverless as interchangeable. Even wikipedia does not differentiate. Yet some people in the field make a point of the differences (e.g. Alain Kornhauser). If I understand these differences correctly, a self-driving car is not as advanced as driverless, in that driverless doesn’t have the back-up of a person taking control, and self-driving might. Driverless taxis are not merely self-driving, they pick up passengers and may be personless. In SAE terms, driverless is Level 5, while self-driving is Level 4 or below.
Generally, the difference between automatic (or automated) and autonomous is the degree of human intervention. An automated car does not have the level of intelligence or independence that an autonomous car has. So driverless and autonomous are nearer to synonyms, as are self-driving and automated. A truly autonomous car would decide on destination and route as well as control within the lanes. An automated car would follow orders about destination and route, and may only adopt some lane-keeping or car-following guidance.
Nevertheless, I do not believe these differences can be preserved linguistically, even within the profession, the broad misuse and confusion will drown small differences of meaning.
Etymology online gives the following:
autonomous (adj.) 1800, “pertaining to autonomy;” 1804, “subject to its own laws,” from Greek autonomos “having one’s own laws,” of animals, “feeding or ranging at will,” from autos “self” (see auto-) + nomos “law” (from PIE root *nem- “assign, allot; take”). Compare privilege. Used mostly in metaphysics and politics; see autonomic. Related: Autonomously.