Reporters covering Secretary of State Cyrus Vance got so sick of his describing his four-day visit here as "exploratory" that they organized a betting pool on how many times he would use the word.

Then the Chinese started to use "exploratory" also, throwing the pool organizers into a tizzy and proving that Peking and Washington had at least been able to agree on a mutual exchange of modest public expectations.

After the high hopes of the Nixon trip to Peking and the Shanghai Communique of 1972 and the stall in relations brought about by Watergate and the death of Chinese foreign-policy architect Chou En-lai, a new administration in Peking has apparently decided to let a new administration in Washington edge cautiously toward full relations.

Chinese impatience with American foot-dragging voiced earlier this year seems to have dissipated, at least on the surface. Some here think the Chinese were only temporarily irritated at careless statements by President Carter.

Some think the Chinese have simply had time to study the matter and have concluded that Carter does have a problem in persuading Congress and the American people that the Nationalist Chinese island of Taiwan would not be significantly harmed by a switch of relations to Peking.

By giving the cautious Vance a warm welcome here and adopting some of his own language, the Chinese keep Sino-American relations healthy enough for the exchanges of information and occasional coordination of policy in dealing with what they see as the greatest mutual problem - the Soviet Union.

Using typical Chinese code words in his farewell banquet toast before Vance flew to Tokyo this morning, Foreign Minister Huang Hua underlined the importance the Chinese put on U.S. ties as a way to fend off the Soviets.

"As we have repeatedly pointed out," Huang said, "China and the United States have different social systems, or two sides have different ideologies and naturally there are differences of priciple between us, but in the present international situation our two countries face questions of common concern and have quite a few points in common."

Vance and his Chinese counterparts clearly had many disagreements during these talks as the gargon "frank and candid discussion" indicated.

The disagreement sare unlikely to have been more serious than other "frank" Sino-American exchanges in the past. Vance's comments and the consistency of Chinese foreign policy over the last several years suggest that the exchanges followed a course not unlike the lively argument Vance had with Vice Premier Teng Hsiao-ping when Vance visited China as a private citizen in 1975.

Then Teng, who also saw Vance during this trip, made light of Vance during this trip, made light of Vance's concern over the proliferation of nuclear weapons. Vance complained in that same meeting of Chinese propaganda's distorting U.S. policy abroad. At that earlier meeting Teng reaffirmed China's claim on Taiwan, but he put the question of the offshore Chinese provicce into revealing perspective:

"You will note that we have said nothing about your base on Diego Garcia. We view such issues from the level of global strategy. In comparison, such matters as 'kith and kin' on Taiwan and the controversy about the mayor's delegation" - disputes that affected Sino-American cultural exchanges - "are just 'chicken feathers and onion skins,' and not important. The 'polar bear' is much more important," Teng said according to a paraphrase of their 1975 conversation published by the Rockefeller Foundation which sponsored Vance's earlier trip.

This April a senior Foreign Minister official here told two visiting American reporters, "We haven't yet found any sign on the part of the U.S. that they've made up their minds to discuss normalization of relations . . . For example, while (Carter and Vance) say they support normalization, they won't discount their old friend Chiang Ching-kuo," Taiwan's president.

Even before Vance arrived here, he seemed to have soothed this Chinese annoyance. In his June 29 speech to the Asia Society he significantly failed to mention the U.S. mutual defense commitment to Taiwan.

Of normalization of relations with Peking, he said: "We recognize that progress may not be easy or immediately evident. But this administration is committed to the process." The Communist press in Hong Kong usually a good barometer of opinion in Peking, reacted favorably to the speech.

But the good feelings Vance apparently carried away from here will be of little use in tackling the complex legal and political issues that stand in the way of normalization.

Vance gave no hint that the Chinese had backed down from their insistence that they have the right to invade Taiwan if they wish. Members of Congress say they need some sign from Peking, indirect or otherwise, that Taiwan will remain untouched in the near future before they can endorse ending the U.S. military commitment to the island.

Then there is the nasty thicket of crucial technical agreements with Taiwan, such as control of nuclear fuel-processing plants and civil aviation rights.

Solving such puzzles will take time, so Vance must have been happy to hear Chinese Communist Party Chairman Hua Kuo-feng speak well of the Carter administration's decision to do no more than "explore China and get to know the leaders of China."

"That's very important," one Chinese guide told a reporter this week "that means 'exploratory' is okay."