A hard currency is one that is widely trusted, stable in value, and freely accepted in international trade and as a reserve; a soft currency is unstable, weak, and not readily accepted outside its home country.
The distinction (hard equals strong, stable, freely accepted; soft equals weak, unstable) and the typical examples of hard currencies are testable external-sector facts.
Hard currency (stable, globally accepted reserve currency like the US dollar) versus soft currency (weak, unstable, not widely accepted); hardness is about trust and stability, not the physical note.
Hard currency is stable and globally accepted (US dollar, euro, yen); soft currency is weak, unstable, and not widely accepted.