Hard money is money issued with the backing of gold or other very credible assets. This type of money issue was in practice nearly one century back. Confidence in the newly established paper currency was an issue during that time. Here, many central banks and policy makers advocated keeping of proportional gold reserves while issuing new currencies. An apt example for hard money is the gold coin itself.
But the system became outdated towards the middle of the 20th century. Here, money supply has to be expanded to meet the transaction demand of the expanding population as the volume of goods and services transaction exploded. This necessitated increased supply of money. The central banks were unable to get gold to match the issue of new currencies. Hence the hard money concept has lost its relevance.
Soft money is just paper currency backed by government bonds. Here money is printed without keeping adequate reserves like gold in proportion to the newly issued money.
Hard money avoids the risks of inflation, whereas the element of inflation is higher under soft money.