The two domains are the Archaea (Archaebacteria) and the Bacteria (Eubacteria).
Archaea are the prokaryotic cells, unlike the Bacteria and the Eukarya, the Archaea possess the membranes comprising of branched hydrocarbon chains connected with the glycerol by the ether linkages. The Archaea generally thrives in extreme environments and comprises methanogens, hyperthermophiles, and halophiles.
The Bacteria are also prokaryotic cells, and unlike the Archaea and the Eukarya, the cell walls of Bacteria comprises of peptidoglycan. Bacteria comprise cyanobacteria, mycoplasmas, Gram-negative bacteria, and Gram-positive bacteria.