Hydrogen ion is recommended by IUPAC as a general term for all ion

Ion

An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

s of hydrogen

Hydrogen

Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 and its isotope

Isotope

Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

s.
Depending on the charge

Electric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

 of the ion, two different classes can be distinguished: positively charged ions and negatively charged ions.

Under aqueous conditions found in biochemistry

Biochemistry

Biochemistry, sometimes called biological chemistry, is the study of chemical processes in living organisms, including, but not limited to, living matter. Biochemistry governs all living organisms and living processes...

, hydrogen ions exist as the hydrated form hydronium

Hydronium

In chemistry, a hydronium ion is the cation , a type of oxonium ion produced by protonation of water. This cation is often used to represent the nature of the proton in aqueous solution, where the proton is highly solvated...

, H₃O⁺, but these are often still referred to as "hydrogen ions" or even "proton

Proton

The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s" by biochemists.
When hydrogen loses its electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

, the following cations can be formed:

• Hydron
  Hydron (chemistry)
  In chemistry, a hydron is the general name for a cationic form of atomic hydrogen : most commonly a "proton". However, hydron includes cations of hydrogen regardless of their isotopic composition: thus it refers collectively to protons , deuterons , and tritons...
  
  : general name referring to the positive ion of any hydrogen isotope (H⁺)
• Proton
  Proton
  The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
  
  : ¹H⁺ (i.e.