the Three-Domain System

Bacteria and Archaea are classified as Prokaryotic organisms (single-cell organisms that lack a nucleus and membrane-bound organelles). Bacteria and Archaea have a cell wall and NO nucleus.

Anatomy of a bacterial cell- Source: ThoughtCo.

Eukaryota are classified as Eukaryotic organisms (single-cell and multi-cellular organisms). The cells in this category have a nucleus and membrane-bound organelles.

The bacteria “genera” Aquifex, Thermotoga, Bacteroides Cytophaga, Planctomyces, Cyanobacteria, Proteobacteria, Spirochetes, and Green Filamentous bacteria are classified as “gram-negative” bacteria.

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Source: ThoughtCo.