Final answer:
The false statement about the differences between cells is that prokaryotic cells have a nucleus, while eukaryotic cells do not; in truth, it is the other way around.
Step-by-step explanation:
The question asks which of the following statements about differences between cells is NOT true. The correct answer is C) Prokaryotic cells have a nucleus, while eukaryotic cells do not. This statement is false because prokaryotic cells lack a nucleus and eukaryotic cells have a nucleus. In contrast, all cells do indeed have a cell membrane, stated in option A, which is true. In option B, it is correctly stated that plant cells have a cell wall while animal cells do not. Lastly, D) is true because some cells do have specialized structures for specific functions, as seen in the various organelles within eukaryotic cells.