From my "Official Nintendo's Player's Guide" for Final Fantasy "III":
"Special Low-Energy Attacks
All of the characters have special attacks that they execute only when their HP is running dangerously low--and then only randomly. When a party memer's HP is so low that they kneel to conserve energy between turns at attack, select the Fight command. Occaisonally, the weakened character will respond by using his or her special attack. The chart below shows each member's special, low-energy attack."

So if anything, they were originally called "Low-Energy Attacks"... not quite a fitting name if you ask me.

Edit: Holy crap this Strategy Guide is old!