Nanoparticles and nanonplates are different geometrical structures from graphine which is mostly a single layer of graphite. Nanoparicles have very limited dimensions in the three direction of the space. While nano plate is a structure which is extended an a plane that in a two dimensions while its dimension in the third dimension vertical to its plane is plane is much less than its plane extension.
The first one can be treated as quantum dot where the other one can be considered as a two dimensional gas.
The applications stems from their quantum mechanical properties.
For the applications in the DSSC please refer to the review paper:Article Graphene-Based Dye-Sensitized Solar Cells: A Review