Some short-term memories--such as part of a conversation--become part of long-term memory, but many vanish quickly, perhaps because there is no value to keeping them.
A variety of conditions, including simple aging, can diminish or destroy short-term memory, while leaving long-term memory intact.
One of pioneers of short-term memory research is George A. Miller, who wrote the classic article The Magical Number Seven, Plus or Minus Two.
See also: amnesia