The differences between these two groupings has to do with the presence or absence of a nucleus and cell organelles.
Prokaryotic organisms lack a nucleus.
They possess DNA material but it is not enclosed within a membrane system called the nucleus. These organisms also lack cell organelles such as chloroplasts or mitochondria. Organism included in the prokaryotes are the bacteria and blue-green bacteria. Eukaryotic organisms posses the nucleus and cell organelles. If a cell wall is present it is not of the peptidoglycan type.