Broensted Acids and Bases: They are not Substances but Molecules or Ions!
For chemistry education we are discussing mainly two concepts of acids and bases: theories of Arrhenius and Broensted. For the first theory, dissociation into ions is generally discussed: acidic solutions contain H+(aq) ions, alkaline solutions contain OH-(aq) ions. This theory therefore deals with substances, which are referred toas acids and bases – it would be even better to take the logical names "acidic and alkaline solutions". If both solutions are mixed in equivalent quantities, the H+(aq) ions react with OH-(aq) ions to form H2O molecules, while the other ions remain in solution (in exceptional cases an insoluble salt may precipitate: sulfuric acid solution reacts with barium chloride solution to solid white barium sulfate and water). The Broensted theory defines proton transfer: a molecule or an ion transfers a proton to another molecule or ion, two conjugated acid-base pairs are involved. Thus, Broensted acids and bases are no more substances, but individual types of particles. Due to the autoionization of H2O molecules (not "autoionization of water"), the following equilibrium exists:
H2O + H2O ⇌ H3O+(aq) + OH-(aq)
Through this protolysis it is more advantageous to argue rather with H3O+(aq) ions than with H+(aq) ions. In this theory there are still ampholyte particles which react as acid or as base particles depending on the reaction partners: H2O molecules, NH3molecules , HSO4-ions – water, ammonia or sodium hydrogen sulfate cannot be regarded asampholytes. The original publication of Broensted  from 1927 makes clear that acids and bases should be molecules or ions, but not substances.