The relationship between these theories is illustrated in the figure at the left.
In acid-base chemistry, the hydrogen ion is often called and written as a proton (H+), but in fact it exists in a variety of hydrated forms that include H3O+, H5O2+, H7O3+. When we write H+(aq) or H3O+(aq) we are referring to the dynamic equilibrium mixtures of these forms of protonated water.