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.