A 'particle' is usually defined as a small object that behaves as a whole unit in terms of its transport and properties. A 'grain' is , again, one of the basic concepts in the solid state physics.It is also termed as crystallite. It is a domain of a solid state matter that has the same structure as a single crystal. In nanotechnology, for example, the 'particle' and 'grain' are very distinct things. However, in areas such as powder technology, the two definitions often overlap, with 'particle size' and 'grain size' being the same thing.
Rigorously though, a “grain” is a region of many particles, with an uninterrupted crystal structure (characterized by a repeating unit cell).
Crystallite Size is Different than Particle Size. A particle may be made up of several different crystallites or just one crystallite so in this case (particle size = crystallite size)
Crystallite size often matches grain size, but there are exceptions
Crystallites are coherent diffraction domains in X-ray diffraction.
Particles are chunks/pieces (usually very small, below 1 mm) of solid matter, ensembles of atoms. Particles can be as small as two atoms (the nitrogen particle for example, N2)
Grains are volumes, inside crystalline materials, with a specific orientation.
Particles can be polycrystalline, single crystal or amorphous. A 100 nanometer particle of gold, for instance, can be made of:
This comparison is different for different samples. For nano particles both quantities could be the same. I have recently watched a video on this topic. It is very effective and easy to understand.
You may find this useful - https://www.youtube.com/watch?v=hjUp2pkONRM