What is the main difference between Quantum Clusters and Nanoclusters?
Short answer: "quantum clusters" is not widespread and likely confusing. I'd suggest "small nanoparticles" or perhaps "metal nano clusters."

I can't comment on optical shifts, but many of these properties are distinct to the particular material and the onset of quantized energy levels in that material. So I doubt you can simply combine properties of quantum dots and nanoparticles.

I asked a colleague who synthesizes gold nanoparticles. She hasn’t heard anyone use the term "quantum clusters" and thinks people would find it very confusing.

Typically the usage:


Quantum Dots refer to semiconductor nanoparticles, e.g., $\ce{CdS}$ or $\ce{PbSe}$ etc.
Nanoparticles refer to nanometer-sized particles of basically anything (proteins, polymers, metals, etc.)
Clusters refer to very small particles (i.e., &lt;1-2 nm diameter) with well-defined numbers of atoms (i.e., a few hundred at most). There is an IUPAC Gold Book definition:


  A number of metal centres grouped close together which can have direct metal bonding interactions or interactions through a bridging ligand, but are not necessarily held together by these interactions.



For reference, Wikipedia suggests nanoclusters are aggregates of nanoparticles. I don't think that's in common use, but certainly it suggests your suggested term would be very confusing.