When an acid neutralizes a base (or vice versa) it forms a "salt"salt, and water (typically we specify a water solvent when we speak of "acid-base chemistry"acid-base chemistry).
Consider the simplest acid-base reaction:
NaOH(aq) + HCl(aq) rarr NaCl(aq) + H_2O(l)NaOH(aq)+HCl(aq)→NaCl(aq)+H2O(l)
Certainly, sodium chloride, unquestionably a salt (a binary compound of a metal and a non-metal), AND water have been formed as the result of neutralization of HO^-HO− and H^+H+. I write (aq)(aq) beside the products and reactants, because in solution these species are ionized, e.g. HO^-HO−, Cl^-Cl−, Na^+Na+ etc.
The acidium species is often represented as H_3O^+H3O+; this again is a representation. As fas as anyone knows this is a cluster of water molecules, with an extra H^+H+, i.e. H_5O_2^+H5O+2, H_7O_3^+H7O+3. If we treat it as H^+H+, or H_3O^+H3O+, we are able to do calculations and stoichiometry.
All (aqueous) acid base chemistry can be represented by the word equation:
"Acid + base " rarr" salt + water"Acid + base → salt + water