Acid-Base Theories

H represents hydrogen atom (1 proton/1 electron)
H+1 represents hydrogen ion (1 proton/No electron)
p+1 represents free proton
We will make no distinction between H+1 & p+1
(H+1 actually represents nuclei of 1p, 1p/1n, 1p/2n)

Since it is impossible to have free proton in water,

terms hydronium ion (H3O+1), hydrogen ion (H+1), and free proton (p+1) are often used interchangeably.

Arrhenius Theory
Arrenhius proposed (1883) that ionic compounds dissociate and can become free ions acting as separate entities in solution.
ACID: Produces H+1 in Water
BASE: Produces OH-1 in Water

HCl(aq)H+1 + Cl-1
HNO3(aq)H+1 + NO3-1
NaOH(aq)Na+1 + OH-1
NH3(aq)NH4+1 + OH-1
(Although NH3 does not contain OH-1, hydroxide ions form when added to water)

The Arrhenius theory also allows acid and base to neutralize each other producing salt & water:
Acid  +  Base Salt + water
H+1(aq) + OH-1(aq)H2O(l)
HCl(aq) + NaOH(aq)NaCl(aq) + H2O(l)

Arrenhius theory most limited of the 3 theories; it requires reactions be aqueous and applies only to substances producing H+1,OH-1,or H2O.

Bronsted/Lowry Theory
Bronsted & Lowry proposed a new acid-base theory in 1923.

When acid transfers proton it becomes conjugate base (CB); when base accepts proton it becomes  conjugate acid (CA). (See Conjugate Acid/Conjugate Base)

Since protons are always transferred in the Arrenhius theory, all Arrhenius acid/base reactions are also Bronsted-Lowry acid/base reactions.
Bronsted-Lowry theory expands Arrenhius theory to include any proton transfer (water not required).

Lewis Theory
In 1938 Gilbert Lewis proposed a more general acid base theory.

ACID: Accepts pair of electrons for sharing
BASE: Donates pair of electrons for sharing

The product of Lewis acid-base reaction referred to as adduct. The proton itself can act as Lewis acid. Lewis expands acid/base reactions to include many substances without H in formula.
F3B+:NH3F3B:NH3Explained by Lewis but not Arrenhius or BL
acid   base        adduct

:NH3 Base because of lone pair
F3B   Acid because of empty orbital