To understand why today's most important caller at the White House is the prime minister of mainland China, remember that no American president ever had such a warm and friendly welcome in Moscow as Richard Nixon did when he went there - after first going to Peking.
Prime Minister Zhao Ziyang is welcome at the White House today for many reasons. One is that the Chinese in October held a third round in a series of talks with the Soviets.
That third round was distinguishable from the two previous rounds. The first, which was held in Peking in October 1982, lasted two weeks. There was no ''socializing'' between the two delegations during the talks. And there was no communique at the end. The second round, in Moscow, in March of 1983 was similar. There was no ''socializing'' and no communique.
But Round 3 in Peking from Oct. 6 to 30 lasted over three weeks, did include ''socializing,'' and was concluded by a communique. The communique disclosed only subtle changes in the Soviet-Chinese relationships. The parties agreed to increase trade and improve tourist and cultural exchanges.
But no agreement had been reached on China's three main conditions for a return to ''normal'' diplomatic relations between Peking and Moscow. Those are that Moscow cease supporting Vietnam's military presence in Kampuchea (Cambodia) , withdraw Soviet troops from Afghanistan, and reduce Soviet missiles and troops along the Chinese frontier.
At present Moscow maintains 57 Army divisions and 180 medium-range SS-20 nuclear missiles along the Chinese border.
China plays its cards in the classic diplomatic manner. It has wanted trade with the West, access to the technology of the West, and support against Moscow. It was getting all these things in gradually increasing degree from Presidents Nixon, Ford, and Carter.
The steady improvement in China's relations with the US was suspended when Mr. Reagan arrived at the White House with ideas about reviving formal US ties with Taiwan instead of with Peking. He was gradually talked out of doing anything so drastic but did insist on continuing to supply modern weapons to Taiwan.
President Reagan was persuaded in late 1982 or early 1983 that having mainland China ''on our side'' instead of moving back toward Moscow was desirable. The Pentagon did not want those 57 Soviet divisions moving back from the center of Asia toward Europe.
In February Secretary of State George Shultz went to Peking to assure the Chinese that Washington wished to resume the relationship of the Nixon-Ford-Carter years. On May 5 a contract was signed for American Motors Corporation to build four-wheeled vehicles in China. On May 21 US Secretary of Commerce Malcolm Baldrige was in Peking talking trade. On July 30 a new trade agreement was signed. On Aug. 6 the Chinese granted drilling rights to two American oil companies.
At that time the Chinese were invited to Washington and President Reagan accepted an invitation to Peking. The trip is scheduled for April, which will give him his turn to be photographed on the Great Wall as the presidential campaign is getting under way.
But the Chinese, having been upset by the two-year slowdown in association with the US (1981 and 1982), responded by allowing the Soviets to send that delegation to Peking in October 1982 and keeps the dialogue going as a gentle reminder to Washington that they always have the option of turning to Moscow again.
During that third round of Chinese-Soviet talks in October, the Soviet delegation was headed by Deputy Soviet Foreign Minister Leonid F. Ilychev. Mr. Ilychev took time out during the talks for a boat trip through the Yangtze River gorges. Chinese Deputy Foreign Minister Quian Qichen went along as host.
When 20 Soviet tourists arrived in China during the Ilychev visit, the Chinese press reported that it was the first such visit in ''two decades.'' They sent back 14 Chinese tourists to Moscow, also a first in ''two decades.'' But they sent 14, not 20. They are ''playing it cool'' with both Moscow and Washington.