The term pit bull refers to a wide variety of animals with squat, muscular bodies and steel-trap jaws descended from the fighting bulldogs of 19th-century England. They are known alternately as American pit bull terriers and American Staffordshire terriers, and commonly include mixtures with Staffordshire bull terriers, bull terriers and bulldogs. All have in common a genetic history of being bred for fierce combat with other animals or other dogs.

Few definitive figures on dog bites are available. But the Humane Society of the United States says that since July 1983, pit bulls have been responsible for 20 of the 28 deaths after dog bites in the nation, including all five this year. The breed accounts for perhaps 1 percent of all dogs in the nation.

The most publicized recent attack came in June when a chained pit bull guarding a marijuana crop in California killed a 2 1/2-year-old boy. In the past week alone, a 3-year-old Ohio girl lost part of her nose after she was attacked by her family's pit bull and a Michigan man was charged with assault with a deadly weapon when his pit bull attacked a 12-year-old girl.

For victims like Ms. Smith, 45, who still suffers nerve damage from the attack, the emotional effects linger long after the assaults. ''I can't remember the pain, I can only remember the terror. I remember thinking, they're killing me and I can't stop them,'' said Ms. Smith, who lives in Houston. Such incidents have stirred intense emotions around the country. ''From the testimony we heard here, I think we should treat them like bears or tigers,'' said Ethel Sandoval of Tijeras, N.M., a city that banned pit bulls after a 9-year-old girl almost died after being mauled by four pit bulls in 1985. Some Areas Ban Pit Bulls

Largely as a result of pit bulls, more than 600 communities have requested information on animal control ordinances from the Humane Society this year, said Randall Lockwood, its director of higher education.