It is not so much privacy as solitude that Jimmy Carter pursues with typical intensity while on vacation.

Phil Wise, who has known Carter since Wise was a boy in Plains, Ga., taking Sunday School lessons from the future president, finds that in keeping with the character of the man he knows so well.

"There's no doubt that he does like to get off by himself," says Wise, the president's appointments secretary. "Anyone who goes as hard as he does just needs that."

For the past four days Carter has had much privacy, and solitude when he wanted it. He is staying on Sapelo Island, about 30 miles north of here, free to ramble through a huge villa shared only with his wife, Rosalynn, and daughter, Amy.

The island's shoreline is being patrolled by five Coast Guard vessels, which have kept the cameras of the television networks at a safe distance. On Friday, the cameras caught a brief glimpse of the president, alone in a jeep, exploring the island. He was not seen again until today, when he attended church services.

The White House has put out only the briefest of announcements about Carter's activities. He has rested in the villa and read. He has walked the beach with his daughter. He has gone fishing with Amy and two old friends and Saturday he jogged and went on a picnic with friends.

Some people relax by doing nothing. But, according to Wise, Carter relaxes by throwing himself into leisure-time pursuits with the same intensity he is known for around the White House.

Wise speaks of the president's "total concentration" when, after a long absence, he resumed the art of fly fishing last August while on a vacation along the Salmon River in Idaho.

Even a quiet stroll can be an exercise in concentration for Carter. Soon after moving to the White House, the president ordered each of the trees on the grounds labeled so he could study and remember them. By now, Wise suspects, Carter has memorized most of the types of vegetation that grow around the Executive Mansion.

"It doesn't make that much difference what he does so long as he can build a skill and concentrate totally on it," Wise said.

Still, like anyone, Carter has his favorite pasttimes. He is certainly the the most avid tennis player of any recent president. And he is naturally drawn to the water and places like Sapelo Island, where he can fish and swim.

Other presidents have had their favorite pasttimes and places to go. Often, this meant going home.

Franklin D. Roosevelt, crippled by polio as a young man, could not be an active sportsman like Carter. He most often vacationed at his home in Hyde Park, N.Y., and at the "Little White House" resort in Warm Springs, Ga.

Harry S Truman traveled frequently to his home in Indenpence, Mo., and vacationed in the winter at Key West. Fla. Dwight D. Eisenhower took long fishing and golf vacations around Denver, but spent more times at his farm in Gettysburg, Pa. John F. Kennedy's favorite vacation spots were family quarters in Hyannisport, Mass., and Palm Beach, Fla., where he could golf, sail and swim. For Lyndon B. Johnson, vacation invariably meant a trip to the LBJ Ranch in Johnson City, Tex.

Richard M. Nixon and Gerald R. Ford were not drawn "home" as such. Nixon often relied on the largesse of his wealthy friends. who introduced him to the splendor of Key Biscayne, Fla., and San Clemente, Calif., where his favorite activities were swimming and walking the beach. Ford had two leisure-time passions-skiing in Vail, Colo., where he had long maintained a second home, and golf in Palm Springs, Calif.

Carter is different from these recent predecessors in several respects. Three weeks after his inauguration, he traveled to his home in Plains, Ga. It was the first of what was assumed would be many trips to Plains. But like so many assumptions about Carter, it proved to be wrong.

The president still spends Christmas in Plains, but otherwise the trips there have been few.The tiny Southwest Georgia hamlet is hardly a vacation mecca, and since the coming of the Carter presidency has been overrun with tourists and tacky souvenir shops. It offers neither privacy nor solitude.

Without a ready-made vacation oasis like a ranch in Texas or a family "compound" along the sea coast, Carter has had to turn elsewhere.

Where he turn elsewhere.

Where he turned was here, Georgia's "Golden Isles," which stretch from Savannah south almost to the Florida border. He came to these islands often as governor and before. After election day in 1976, it is where he chose to rest after his 2 1/2-year pursuit of the presidency. He has been to these islands four times as president.

Carter, like Nixon, has enjoyed the use of facilities provided by the wealthy. Those earlier vacations here were spent on St. Simons Island, south of Sapelo Island, at a plantation owned by Smith Bagley, heir to the R. J. Reynolds tobacco fortune. Bagley's indictment last month on fraud and stock manipulation charges effectively ended the usefulness of his Musgrove Plantation as a presidential retreat.

But Bagley has never been to Jimmy Carter what Bebe Rebozo was to Richard Nixon. Rebozo was confidant and constant companion, while Bagley has served as temporary landlord, never a part of the presidential entourage.

Carter, in fact, does not have an entourage while on vacation, and he does not seem to need one. Truman loved to play poker and Eisenhower bridge-both more social than solitary pursuits-and Ford enjoyed hobnobbing with the wealthy businessmen who flock to Vail and Palm Springs in season, when he was also there.

Carter has two old friends in nearby Brunswick, Ga.-Carlton Hicks, an optometrist, and Jimmy Bishop. a lawyer. They are not staying on Sapelo Island, but are available if the president wants their company.

"You know, he's not like us."

The speaker was part of the White House advance party, which precedes the president on any trip, explaining what it takes to put a presidential vacation together.

"He can't go walking around to figure out what he can do," the aide said. "He does what he does spontaneously, but suppose he wants to go water skiing and there is no boat. I wouldn't want to be the one to tell him."

To guard against that possibility, the advance team scours the vacation area, reporting to Wise on the recreational possibilities. The appointments secretary, in turn, informs the president, estimating for him how long it would take the White House staff to prepare for whatever activity may interest him.

Once in place in a vacation spot, Wise said of himself and the immediate personal staff that accompanies Carter everywhere, "We try to see him as little as possible."

Around the White House, Rosalynn Carter is credited with convincing the president to ease off more often from his concentration on work.

There is no telling what will turn a president on. For Eisenhower it was bridge and golf. For Kennedy, it was swimming and sailing. For Carter, it is fishing and tennis.

And, then, there was Calvin Coolidge, as reported 25 years ago by Harold Hinton in The New York Times Magazine:

"He hit the White House with no hobbies at all," Hinton wrote of Coolidge. "He got up early and took walks. Then, some enterprising manufacturer of athletic goods sent him an electric horse. This was a device the president straddled on a saddle, while machinery jiggled and joggled him at various rates of discomfort supposed to simulate a horseback ride. Mr. Coolidge adored it." CAPTION: Picture, EASTER SOJOURN-President and Mrs. Carter meet members of First African Baptist Church congregation after services on Sapelo Island, Ga. AP