In this case, they mean particles they have hit with a laser to split into superposition, so "quantum particles" = "particles in superposition".

Just a layman but whenever I read that, I interpret it as "particles exhibiting quantum phenomena", like superposition or entanglement.

This would be unlike classical particles which does not exhibit these effects.

I guess, this is a shorthand for "particles studied in quantum physics."

objects described by wavefunctions