Does the Prius use an Atkinson cycle engine, or a Miller cycle engine?

The key insight in both of those designs is to have an effective compression stroke shorter than the effective expansion stroke.

The original Atkinson design did that with weird connecting rods. We definitely have nothing like that.

Miller's 1957 design also had some specifics we don't have.

https://www.curbsideclassic.com/blog/the-atkinson-and-miller-cycle-engines-not-exactly-how-they-started-out-to-be/

What we've got, essentially, is a variant of a bog-standard Toyota Otto-cycle engine, with the intake valve timing tweaked to shorten the effective compression stroke.

So, it uses the same key idea common to Atkinson's and Miller's designs, but isn't really either of those exactly.

It's often referred to by the name Atkinson, probably because that was the earlier appearance of the key idea.

 

Atkinsonized Otto is best descriptive name for it. The Atkinsonized term gets used at times when talking about it. Never came across chargeless Miller in reference to the engine.

Those are another point of efficiency improvement. They reduced lateral movement of the piston as it traveled, which reduced its friction against the cylinder walls.

Don't know if it was ever offered outside Japan, but Honda had a true Atkinson engine in a natural gas stationary power station for buildings.

 

A Miller-cycle engine requires a supercharger, so the Prius absolutely is not a Miller.

It helps to mentally separate the theory of the cycle from the mechanism used to achieve it.

Atkinson's theory was to increase engine efficiency by varying the size of the combustion chamber during different parts of the combustion cycle. The mechanism he used to achieve this goal was overly complex due to the (lack of) technology available at the time. All he had to work with were complicated linkages.

Fast forward several decades.

The introduction of new technologies allowed engine designers to build engines on Atkinson's core theory, but without the complicated linkages. These would most accurately be called modified Atkinson-cycle engines.

The problem with these engines is their inability to produce power quickly. Miller's solution was to take a modified Atkinson-cycle engine and stick a supercharger on it. That would help increase power quickly, but still allow for high efficiency once the engine was up to speed. Toyota's solution was to take a modified Atkinson-cycle engine and connect it to electric motors to give power quickly at low speeds.

Toyota would also use variable valve timing to allow the engine to act more like a standard Otto-cycle engine when needed. In fact, most(all?) modern automotive engines are effectively Otto/Atkinson hybrids. Variable valve timing allows the engines to be pure Otto-cycle when full acceleration is needed, but transition to modified Atkinson when up to speed for higher efficiency. It's just that Toyota hybrids are adjusted to lean more heavily to the Atkinson side of the spectrum than their non-hybrid sibling engines. (i.e. M20A-FXS vs. M20A-FKS)