Bacteria and fungi Similarity
There exists very little similarity between Bacteria and Fungi as a whole. For starters, Bacteria are prokaryotes without any defined nuclei. Fungi are Eukaryotes, having a defined cellular nucleus, with the genomic DNA bound by a defined nuclear membrane. The modes of cellular metabolism are vastly different and so is the mode of reproduction. Very few fungi like Saccharomyces and Candida reproduce via binary fission akin to how Bacteria reproduce. A vast majority of Fungi reproduce via sporulation (form spores to preserve and transmit genetic material). The ribosomal content of Bacteria and Fungi are also different which directly translates to difference in the proteins being produced for biosynthesis pathways. It also means that they necessarily did not have a common ancestor.
Bacteria have a defined cell wall and so do the Fungi. But the composition of the cell walls are entirely different. Even the cell membrane compositions vary significantly. Bacteria adhere completely to the mitotic mode of cell division whereas Fungi can undergo mitosis during normal conditions and can form spores via meiosis during stressed conditions.
The most important difference is the presence of Mitochondria in Fungi. Bacteria lack a mitochondria for cellular respiration. Mitochondria in Fungi and other Eukaryotes drive the cellular respiration by producing ATP (the energy currency). ATP in Bacteria is produced in different manners depending on the habitat and species of the Bacteria.