What is the difference between Archaea and Bacteria?

Both bacteria and archaea have different Ribosomal RNAs (rRNA). Archea have three RNA polymerases like eukaryotes, but bacteria have only one. Archaea have cell walls that lack peptidoglycan and have membranes that enclose lipids with hydrocarbons rather than fatty acids (not a bilayer). These lipids in the membranes of archaea are unique and contain ether linkages between the glycerol backbones rather than ester linkages. Archaea resembles eukaryotes more than bacteria. Their ribosomes work more like eukaryotic ribosomes than bacterial ribosomes.

These two microorganisms also differ in genetic and biochemical ways. Only within the last couple of decades, archaea were recognized as a distinct domain of life. They are extremophiles, meaning they thrive in physically or geochemically extreme conditions. They have similar ecological roles as bacteria. Both of these organisms react to various antibiotics in a different way.

It has to do with ether-linked lipids where Bacteria have ester-linked.

Technically, Archaea are distinguished from bacteria based on differences in  variable sequence regions of their 16s ribosomal DNA.  Beyond that, it's not easy to tell them apart, other than archaea tend to be more often than not, "extremophiles," thriving in places that most bacteria can't handle, e.g. the bottom of the ocean slowly eating the iron in sunken ships like theTitannic, highly acidic or salty environments, e.g. Yellowstone hotsprings, deep sea alkaline thermal vents, etc.

The differences are as profound as between Eukarya and Bacteria - a different type of cell

Archaea constitute a domain of single-celled organisms. These microorganisms lack cell nuclei and are therefore prokaryotes. Archaea were initially classified as bacteria, receiving the name archaebacteria, but this classification is obsolete.

Archaea is old bacteria ?