Prokaryotes mainly arise in unicellular forms and examples of organisms that are prokaryotic is bacteria. Eukaryotes on the other hand arise in multicellular form and examples of eukaryotic celled organisms are fungi, plants, animals and the exception which are protoctist as many of them are unicellular.
As mentioned above the DNA lies free in the cytoplasm of prokaryotes, and lies linear and in a nucleus in eukaryotes. However, in prokaryotes the DNA is ‘naked’ and therefore is not associated with proteins or RNA to form chromosomes. While in eukaryotes the DNA is not naked and is associated with protein & RNA to form chromosomes.
In the two types of cells the ribosomes which are used in protein synthesis are slightly different, in prokaryotic cells the ribosome are 70S and smaller than the 80S larger ribosomes in eukaryotic cells.
In eukaryotic cells the ribosomes may be attached to the endoplasmic reticulum, while in prokaryotic cells there is no endoplasmic reticulum.
When it comes to organelles prokaryotes have relatively few, and the ones present have no envelope surrounding them. Furthermore, prokaryotes have few internal membranes, and if present they are usually only used for respiration or photosynthesis.
On the other hand eukaryotes have many organelles, and many are envelope bounded such as the nucleus or mitochondria. In addition, eukaryotes have a great number and diversity of organelles bounded by single membranes for example Golgi apparatus or lysosomes.
When it comes to respiration, prokaryotes like bacteria use mesosomes, the exceptions being cytoplasmic membranes in blue-green bacteria. While eukaryotes use the organelle- mitochondria, which combines glucose and oxygen in the process of aerobic respiration to give energy.
Eukaryotes in addition have the capabilities to photosynthesize due to organelles such as chloroplast in its cells. While prokaryotes also can photosynthesize but have no chloroplast they create food from membranes which show no stacking in it cells.
Nitrogen fixation is the ability to change the form of nitrogen. Eukaryotic cells do not have the ability to carry out nitrogen fixation, while on the other hand prokaryotic cells do.
The structures of the cell walls and compositions of them are greatly different in the cells. In eukaryotes the cell walls of green plants and fungi are rigid and contain polysaccharides; cellulose is the main strengthening compound in plant walls and chitin in fungal walls, however, there are none in animal cells.
However, prokaryotes cell walls are rigid and contain polysaccharides with amino acids, and murein is the main strengthening compound.
Finally when it comes to movement of the cells, flagellum is used in cells; however the flagellum in prokaryotes and eukaryotes are slightly different. In prokaryote cells the flagella is simple and lacking in microtubules, it is also extra cellular, and it has an average diameter of 20nm.
On the other hand in eukaryotes the structure is complex with ‘9+2’ arrangement of microtubules, it is also intracellular, and the eukaryote flagella also have a diameter of around 200nm.
In conclusion, as seen there are many differences between prokaryotes and eukaryotes, in functions, structure and processes.