The main difference between a eukaryotic and a prokaryotic cell is the presence of a nucleus and organelles in the eukaryotic cell and their absence in the prokaryotic cell. The absence of nucleus and membrane-bound organelles classifies organisms as prokaryotes.
Prokaryotic DNA is not inside a membrane, it is short-stranded and free in a cytoplasm. In eukaryotic cells long tangled strands of DNA is packed in the nucleus and because of the length it is organised in chromosomes.