Plantae: Autotrophic, Multi- or Monocellular, have cell walls as well as a membrane, have a chloroplast making the characteristic green color and to capture sunlight for photosynthesis. Break down generated glucose into it's components.
Animalia: Heterotrophic, Multi- or Monocellular, have a cell membrane made of a phospholipid bilayer, and many mitochondria to aid with movement energy. Feed on plants or other animals. Eukaryotic cells.
Fungi: Heterotrophic, most Multicellular, have a rigid cell wall made of chitin, specialized cells to aid with decomposition of dead organic matter. Eukaryotic cells.
Protista: Can be plant-like, animal-like, or fungus-like. Most are single-celled, may be chemosynthetic or photosynthetic. Eukaryotic cells.
Archeabacteria: Prokaryotic. Do not have nuclei or membrane-bound organelles. Move around using a flagellum to propel itself. Lives in mainly fluid environments (air, water). Separated from Eubacteria due to it's high tolerance of extreme conditions, such as high salinity, no oxygen, burning heat, or freezing cold. Can be chemosynthetic or anaerobic, as well as aerobic.
Eubacteria: Normal, everyday bacteria. Prokaryotic, chemosynthetic, anaerobic, or aerobic. Do not have nuclei or membrane-bound organelles. Mobile using a flagellum to propel itself.
Based on these facts, we can state that the genes of the two organisms had a eukaryotic origin.
We can arrive at this answer because:
Despite having exons, prokaryotes do not have introns in their genomes.
This means that if two organisms have the same sequence of introns and exons, they have a common ancestor, in addition to having their genes originated in a eukaryotic organism, which explains the sequence of introns.
This means that the genetic expression of these two organisms has similarities, even if they are organisms with different biological processes.