Scientists have categoried all life on Earth into three 'domains'. These are: eukarya, bacteria and archaea. The domains bacteria and archaea both contain prokaroytes. Because these groups have experienced different pressures on them (i.e. different environmental conditions like food/energy source, temperature, region of the world), they have developed different cell types.
The main difference between these cell types is that eukaryotes have what’s called a ‘membrane-bound nucleus’ which means that their genetic information is wrapped up, whereas in prokaryotes, their DNA is ‘free’ in the cytoplasm (watery filling of the cell). Importantly, eukaryotes have ‘linear’ (straight) DNA stored in a coiled arrangement, whereas prokaryotes often have circular DNA - or plasmids.