Archaea and bacteria (eubacteria) are single-celled organisms that do not have a nucleus or organelles. Archaea have a distinct evolutionary history and biochemistry compared with bacteria.
Archaea - a domain of single-celled microorganisms. These microbes are prokaryotes. Archaea can survive in extreme and harsh environments like hot springs, salt lakes, marshlands, oceans, gut of ruminants and humans.
Bacteria - a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria have a number of shapes, ranging from spheres to rods and spirals. Eubacteria are ubiquitous and are found in soil, hot springs, radioactive waste water, Earth's crust, organic matter, bodies of plants and animals, etc.