All three definitions describe the same concept, but Lewis Acids are the most broad (and include Arrhenius and Brønsted-Lowry acids).
An acid is a substance that increases the concentration of hydronium ions (H3O+) when added to water--this is the same as saying the concentration of hydrogen ions (H+) in water is increasing.
H2O + H+ = H3O+
An acid is anything that donates a proton to other atoms or molecules. Essentially, any compound that can lose a proton is a Brønsted-Lowry acid, this includes all Arrhenius acids, plus amines (-NH2) and alcohols (-OH).
This is the most commonly used definition.
A Lewis acid is a compound that can accept an electron pair to form a covalent bond. This includes some compounds that do not contain hydrogen.
This includes all Arrhenius and Brønsted-Lowry acids.
Acids (and bases) are chemicals that like to trade particles. In a solution, an acid is a chemical that will release hydrogen ions. Those positively charged particles — also called protons (because a Hydrogen atom without an electron is only a proton) — can disrupt other ionic forces.
This is a problem because hyrdrogen ions can cause other molecules to break apart!
(Helmenstine)
MEASURING ACIDITY
pH is a measurement that describes the concentration of H+ in an aqueous solution.
The pH scale goes from 0 to 14. Anything from 0 to 7 is acidic.
7 is neutral on the pH scale.
EXAMPLES OF PH
“The Ph Scale with Some Common Examples.” PMEL Carbon Program, PMEL, https://pmel.noaa.gov/co2/file/The+pH+scale+with+some+common+examples.