Hydrogen ion is recommended by IUPAC as a general term for all ions of hydrogen and its isotopes.[1]
Depending on the charge of the ion, there are two types: positively charged ions and negatively charged ions.
↑McNaught A.D. and Wilkinson A. 1997. Compendium of chemical terminology. 2nd ed, Blackwell Science. ISBN0-86542-684-8 also online