The difference between protoplasm and cytoplasm is that the former encompasses the cytoplasm and nucleus of a cell, whereas cytoplasm is the semifluid substance found below the membrane of the cell. This means that the difference is minor, as both terms can refer to roughly the same components of a cell with different levels of precision.
Protoplasm is a word that has been phased out of use in modern biology due to its largely inaccurate origin. Nowadays, it refers only to the cytoplasm and the nucleus instead of implying that cells were only containers of protoplasm. Modern science has since discovered that cells are much more complex.
Cytoplasm is the substance that contains the organelles of cells that have a nucleus, surrounding the organelles like the mitochondria, the Golgi apparatus and the cytoskeleton. These components are all a part of a cell in the same way as large organisms have organs, performing vital functions for the cell's survival. For instance, the mitochondria produce energy in the form of adenosine triphosphate for the cell to use, the cytoskeleton maintains the cell's shape and structure, and the Golgi apparatus modifies, packages and sorts proteins for transporting to their cellular destinations later on.