The differences between the Jimmy Carter and the Ronald Reagan presidencies show up in full and sparkling color in the seventh edition of "The Living White House," just published.

The cover of the sixth edition shows the south lawn of the White House at sunset, with people at supper around black-and-white-striped tablecloths at a party the Carters gave for stock car racing drivers and their guests.

The Reagan cover on the new edition also shows the south lawn--with fountains sparkling, flowers blooming, and not a blade of grass out of place, almost too perfect to be true.

Thirty new photographs and 29 text changes and additions update the new edition of "The Living White House." Some 879,000 copies have been sold in its 16 years of publication.

Lonnelle Aikman, of the National Geographic senior editorial staff, wrote all seven editions. The first one was produced in 1966 at the suggestion of Lady Bird Johnson.

"I remember going over to interview Mrs. Johnson on the Truman balcony. She said she had a half-hour to talk to me about the book before President Johnson came home for dinner. Well, he didn't come and he didn't come, and we kept on drinking wine and eating popcorn and talking. Finally at 10 p.m., he made it. And I had my long interview," Aikman said. She researched the other editions at White House parties and events.

The National Geographic's Special Publications Division produces the book as a public service. Profits go to the White House Historical Association for purchase and maintenance of antique furnishings.

Nancy Reagan's foreword recalls that she rolled Easter eggs as a child on the south lawn and dined in the house when Reagan was the California governor. "But," she writes, "there's another side to the privileges that we enjoy here. Since the assassination attempt against my husband, we have become more restricted in coming and going and everyday use of the grounds than any other Presidential family in history. Each time my husband comes home to the family quarters, I greet him with special relief. May tragedies such as those that have afflicted earlier families never again come to this house."

Emphasizing this tragic event, the first picture of the Reagans in the book shows them greeting people on the White House lawn when he returned from the hospital April 11, 1981, after the assassination attempt.

On entertaining, Aikman writes: "President Reagan and his wife Nancy have introduced a bit of California's casual lifestyle, plus a touch of elegance, to today's mansion." And she goes on to note the Reagans enjoy entertaining in the house's movie theater. Among the Reagan party pictures are: Nancy Reagan with diplomatic children, the Reagans with Queen Beatrix and Prince Claus of the Netherlands, with Italian President Allesandro Pertini in the north Entrance Hall, and the egg roll on the lawn, April 12, 1982.

The Carters are by no means banished from the book. "They did the most tremendous amount of varied and interesting entertainment, especially the performances by first-rate top classical musicians," said Aikman. New Carter pictures include the party for the Japanese prime minister on the terrace in 1979 and the Eubie Blake jazz festival in 1978, Amy and her Siamese cat and Joan Mondale and Rosalynn Carter in the top-floor solarium, which the then first lady redecorated.

Nancy Reagan's decoration of the White House is duly described by Aikman, who cites her personal additions to the family quarters: pre-Columbian sculptures, a silver repousse' fire chief's horn made into a lamp base, her Battersea boxes (painted enamel boxes) and movie posters. Aikman says framed photographs of Mrs. Reagan are "in various places" in the president's study and a portrait of Nancy Reagan with her then 2-year-old daughter is in her study.

Nancy Reagan's preference for one-shouldered evening gowns is also noted. Aikman writes that the Reagans' clothes have attracted the most attention of any presidential couple since the Kennedys. "The Reagans' smart riding clothes--made for comfort as well as style--have given a conservative touch to the sometimes raffish cowboy vogue of a few years back. In leisure or formal attire, says one of the President's tailors, he is a perfect size 42 long, while Mrs. Reagan, a trim size 6, can wear any style with ease."

The only picture of the newly redecorated family quarters--one that has appeared in several other publications--is of the Reagans with their shoes off, eating dinner on television tables in his study, redecorated with red-and-white flowered chinz.