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 - can survive in extreme and harsh environments like hot springs, salt lakes, marshlands, oceans, soils, and gut (they facilitate digestion), mouth, and skin of humans. Archaea possess genes and several metabolic pathways that are more closely related to those of eukaryotes and use more diverse energy sources than eukaryotes: from organic compounds to ammonia, metal ions, or hydrogen gas. 

Bacteria - are present in most of habitats, and often live in symbiotic and parasitic relationships with plants and animals. Their biomass is only exceeded by plants. There are about 40 million bacterial cells in a gram of soil.

Animal life is dependent on bacteria for survival. Only bacteria and some archaea  synthesize vitamin B12 and provide it through the food chain.

In humans and most animals, the large number of bacteria exist in the gut and on the skin, they are mostly  harmless or beneficial. Several species of bacteria are pathogenic and cause infectious diseases.