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Archaea are a major evolutionary lineage distinct from bacteria. The cellular comparison here concerns the prokaryotic members of archaea; see two-domain system for broader clade usage. Their biological cells have a nucleoid rather than a membrane-bounded cell nucleus, yet aspects of DNA replication, transcription and biological translation resemble those of eukaryotes. Their characteristic lipids differ chemically from the usual bacterial membrane lipids, and their cell walls, when present, lack peptidoglycan. See OpenStax Biology 2e, 22.2: archaeal distinctions.

Some archaea perform methanogenesis, producing methane as part of their metabolism. Archaea also inhabit ordinary soils and oceans: extreme habitats do not define the lineage. See OpenStax Biology 2e, 22.1: moderate and extreme environments. Woese and Fox's 1977 analysis of ribosomal RNA distinguished the methanogenic group they called archaebacteria from typical bacteria. Their proposed three primary lines of descent were a historical interpretation, rather than the final resolution of deep phylogenetics. See Woese and Fox, 1977: Phylogenetic structure of the prokaryotic domain.

Asgard archaea are an archaeal group important in studies of eukaryotic origins. Molecular comparisons connect their genes to the nuclear lineage of eukaryotes, rather than making modern Asgard archaea the direct ancestors of modern animals or plants. See the original analysis cited under two-domain system.

A clade comprises an ancestor and all its descendants. Membership is about common descent, not a taxonomic rank or a degree of cellular complexity. In a two-domain system, the nuclear lineage of eukaryotes nests within archaea; a group containing only the prokaryotic members excludes descendants and is therefore not that complete clade. See OpenStax Biology 2e, 20.2: clades and shared ancestry.

A eukaryote is an organism belonging to the lineage characterized by a membrane-bounded cell nucleus and extensive cellular compartmentalization. A nuclear envelope surrounds the nuclear genome; nuclear chromosomes are typically linear. Ribosomes perform biological translation outside the cell nucleus. See OpenStax Microbiology, 3.4: nuclear organization and protein synthesis. Specialized biological cells can lose their cell nucleus, as mature mammalian red blood cells do, while remaining parts of eukaryotic organisms; see OpenStax Biology 2e, 40.2: mature red blood cells.

Yeasts, plants and animals are all eukaryotes. Typical cells in these groups have mitochondria, but chloroplasts belong to photosynthetic plant and algae lineages, not to every eukaryote. A cell wall occurs in typical plant and fungus cells but is absent from animal cells. These are comparisons of representative cells, not a checklist every specialized cell must satisfy. See OpenStax Biology 2e, 4.3: nucleus, organelles and representative cells.

The interesting feature is controlled separation: cell membranes and organelle membranes let different cellular processes occupy distinct compartments while membrane transport connects them. The evolution of eukaryotes also involved partnership: mitochondria descend from a bacterial endosymbiosis. Modern phylogenetics supports an archaeal ancestry for the nuclear lineage, alongside this bacterial contribution; see two-domain system. Thus the history of a whole eukaryote cannot be read as the history of just one of its genes.

A prokaryote is an organism whose biological cells lack a membrane-bounded cell nucleus. The DNA of its chromosomes occupies a nucleoid within the cytoplasm. Bacteria and archaea have this cellular organization. Both contain ribosomes that perform biological translation and a selective cell membrane; neither is a bag of unorganized chemicals. See OpenStax Biology 2e, 4.2: prokaryotic organization.

The word prokaryotic describes organization, not a single exclusive clade. Grouping bacteria and archaea by the absence of a cell nucleus is useful for comparing biological cells, but does not establish that they share a more recent ancestor with one another than either does with eukaryotes. See three-domain system and two-domain system for the different ancestry models.

Prokaryotic does not mean membrane-free. Cyanobacteria contain internal thylakoid membranes for oxygenic photosynthesis, despite lacking chloroplasts and a cell nucleus. Many prokaryotes have circular chromosomes, but circular shape and a single chromosome are not defining requirements. See OpenStax Biology 2e, 22.2: bacterial and archaeal structures.

The three-domain system recognizes bacteria, archaea and eukaryotes as three domains. In 1990, Woese, Kandler and Wheelis proposed the domain rank and the names Bacteria, Archaea and Eucarya, using molecular comparisons to argue that the older prokaryote/eukaryote division hid important differences. See Woese, Kandler and Wheelis, 1990: Towards a natural system of organisms.

The associated three-domain ancestry model places the nuclear lineage of eukaryotes alongside archaea, rather than within them. This historically influential interpretation should be distinguished from the two-domain system; listing three familiar groups does not establish three independent primary branches.

The two-domain system recognizes bacteria and archaea as the two primary lineages, placing the nuclear ancestry of eukaryotes within archaea. In this model, archaea as a complete clade includes that eukaryotic lineage; restricting the name to prokaryotic members describes a different grouping. Williams and colleagues' study, published online in 2019 and in a 2020 journal issue, found support for this model and a close relationship to Asgard archaea. See Williams et al., 2020: Phylogenomics provides robust support for a two-domains tree of life.

This updates the interpretation of the 1977 and 1990 classifications rather than undoing their discovery of deep differences between bacteria and archaea. Deep phylogenetic trees depend on the sampled genes, organisms and inference model; the precise closest archaeal relatives and early sequence of events require further evidence. Bacterial ancestry of mitochondria through endosymbiosis is a separate part of eukaryotic history.