Since he had knowingly used his Death Note to extend a human life (a violation of Shinigami law), he was reduced to ash, leaving only his Death Note. Touched by this act, Rem delivered Gelus's Death Note to Misa, since it was her life that he saved.
Since he had deliberately employed his Death Note to prolong human existence (a contravention of Shinigami rules), he was eradicated, leaving only his Death Note. Impacted by this act, Rem transferred Gelus's Death Note to Misa, as it was her life that he had saved.