Final answer:
In cell division, chromosomes are always present and essential for proper DNA allocation, whereas centrioles, which are involved in organizing the spindle apparatus, are not present in all eukaryotic cells such as plants and fungi.
Step-by-step explanation:
In relation to cell division, chromosomes are always present in the cell whereas centrioles are not always present. Chromosomes ensure that each cell receives the proper amount of DNA during cell division, which is critically important for the maintenance of genetic consistency across cells. In eukaryotic cells, chromosomes hold the genetic information that is duplicated during cell division, whether it occurs by mitosis or meiosis. Mitosis leads to the production of two daughter cells that are diploid and genetically identical to the parent cell, each containing the same number of chromosomes as the parent cell.
On the other hand, centrioles are cell structures that are particularly notable during cell division in animal cells. Centrioles help organize microtubules during the cell division process to form the spindle apparatus which is crucial for the movement of chromosomes. However, centrioles are not found in the centrosomes of plant and most fungal cells, emphasizing that these structures are not universally present in all eukaryotic cells.