As defined and explained elsewhere, nucleoid and nucleus are different.
A nucleoid is just a place in the cytoplasm without ribosomes, where dwells a single circular naked DNA molecule containing most, if not all in some case, of the genetic information needed for whole cell life.
Nucleus is different, well-known and well described in many biological books.
Here we have a choice. Talking about the genetic material of the cells we may say that only eukaryotic ones have chromosomes as just described and the prokaryotic types have circular naked DNA molecules, or we may say that prokaryotic chromosomes are different from the ones found in eukaryotes and describe both correctly. Once again scientists tried to find chromosomes in every cell!
Let us go back to the nucleus. It has linear chromosomes, not just one, not just DNA. Most of the eukaryotic cells are born with just one nucleus and therefore cannot divide early in their lives. When they go through DNA synthesis in the S phase of the life cycle, the DNA quantity doubles within every chromosome so that in the phase G2 we still have one nucleus, only about 2 times bigger than the one in G1 phase. No cell division can occur in G2 if the goal is to give birth to 2 fully functioning organisms. Two nuclei are needed before cell division.
The recent eukaryotic cells have a problem the older prokaryotic types did not have: how to duplicate the nucleus? Life being creative they searched and found thetwo parallel solutions: mitosis and meiosis to choose from, according to the end results desired.
For the newly evolved larger cells the life cycle has 5 main phases:
1. The first growth phase called G1 is characterized by a single genetic center, here the nucleus.
2. The phase S where there is DNA synthesis, doubling the amount of DNA inherited at birth.
3. The second-growth phase, G2, is the one where there are two non separate DNA molecules in each chromosome in the nucleus that prepare to duplicate into two smaller new ones within the cell.
4. The fourth life cycle stage of the eukaryotic cell is the nucleus duplication phase which can be mitosis or meiosis at choice. Either one has 4 well-known sub-phases that are prophase, metaphase, anaphase and telophase. At the end of nucleus duplication the cell will have two nuclei and can now divide and be able to give the same amount of genetic information to both its daughters.
5. The cell division phase allows to produce two new smaller cellular organisms, each with its own nucleus.
Eukaryotes did not invent a new way of producing news cells from one. They just use the same process created by prokaryotes: real cell division or cytoplasm division. What they did differently is find a way to duplicate the nucleus.
Primitive cells invented cell duplication and more recent ones created mitosis and meiosis as ways to nucleus duplication that must occur in them before cell duplication.
Most well written and well-known biological books describe mitosis and meiosis as cell division process and yet this is not true. One of the reasons it is not true is because it is well-known that some cells go mitosis, get two or more nuclei they need for their functioning, without dividing. Also, there is no reason prokaryotes duplicate themselves without mitosis or meiosis and only eukaryotic cells need both process to duplicate themselves. The reason mitosis and meiosis occur in more recent cells and not in primitive ones is that both processes deal with something only eukaryote have: the nucleus.