Eukaryotic flagella like those of Volvox do not work on a wheel and axle principle, they flail around like whips. The International Society of Protistologists recommends that they should instead be called cilia, since they are homologous with cilia rather than with bacterial flagella. Etymologically it would make more sense the other way round, since flagella should flail, not rotate, and I think the eukaryotic examples were described first anyway.
That's the bacterial one that rotates like a wheel, yes. Many eukaryotes have a structure that looks superficially similar, but is unrelated and completely different structurally. It doesn't rotate, but is bent back and forth by the movement of the microtubules inside (pic below); kind of like how muscle fibres work.