Quantum dots are semiconductor nanostructures with conduction band electrons and valance band holes. They can reflect different colors depending on their extrication energy level. Carbon dots are made of carbon atoms. Nanoparticle is a general word that can be used for any nanolevel particles such as metal nanoparticles, semiconductor nanoparticles, etc.

Dear Anshu,

Quantum Dots: Nanoparticle of any element or compound having radius less than the excitonic Bohr radius of the particular chemical species. Suppose the excitonic Bohr radius is calculated to be x nm for a certain species. Then any nanoparticle measuring less than x in dimension can be considered as a QD. These are generally zero dimensional spherical particles. So, all the dimensions must be below the Excitonic Bohr radius.  

Nanoparticle: Any zero dimensional (dimensions along all directions in nm range) nanostructures are nanoparticles.

Carbon Dots: Carbon QD may be considered to be a very small region of a CNT (2 D structure) where electron is concentrated (high electron density). Generally their radius is ~10 nm or less.

In a QD, Quantum Confinement effect is observed which brings about variation in the physical (electrical, optical etc.) properties of the material.

Hope this helps!

Thank you Morteza Amjadi, Vinod Kumar and Sayan Dey.

This helps me lot.