The uproar that has spun out of Egyptian President Anwar Sadat's wounded reactions to President Carter's televised comments on the Palestinian question is a case of polarized media diplomacy colliding with the fine shadings, and the subtle dissembling, of professional diplomacy.

This incident, which may require a Carter visit to Egypt to soothe ruffled feelings, may go down in the annuals as a prime example of too-swift, too-simplified, public diplomacy.

On its face, Carter jarred Sadat and many other Arab leaders by his extemporaneous remarks about a Palestinian state in his television interview Wednesday night.

But the reality is that nothing Carter said in expressinghis administration's preference against the creation of a Palestinian state represented any change in the official American position.

The problem was candor and the timing of what Carter said out loud, the over-hard interpretations put on Carter's remarks by the media, and the media demands on Sadat to react immediately.

Carter said that it is his opinion that "permanent peace can best be maintained if there is not a fairly radical, new independent nation in the heart of the Middle Eastern area."

There is every indication that this is the underlying belief, as well, of every moderate Arab leader, especially including the leaders of Egypt, Jordon and Saudi Arabia. They want, at least as much as Carter, to avoid creation of a radical new state in the region, which might jeopardize their own interests and become susceptible to Soviet influence.

But they dare not say so publicly at this time. Their private preference is not far removed from what Carter has advocated, "a homeland or an entity where-in the Palestinians can live in peace," perferably with links to Jordan.

President Sadat, "so far," Carter said, "is insisting that the so-called Palestinian entity be an independent nation." Sadat, while he calls for "a Palestinian state, more often puts his greatest stress on the right of "self-determinaton." This is fact is a more open-ended formulation, with options for the form of self-determination.

The essential issue for the moderate Arab leaders is the achievement of a Palestinian national homeland that will fulfill Palestinian aspirations, without the "homeland" turning into an unguided missile in their midst for the most extreme elements of the Palestine Liberation Organization.

Israeli Prime Minister Menahem Begin's current offer for a peace settlement, however, falls very short of that objective. Among other things, it calls for a continued Israeli military force on the West Bank of the Jordan River and in the Gaza strip. No Arab leader can accept that premise.

It is for this reason that American strategists look on the Begin offer, as Secretary of State Cyrus R. Vance put it on Thursday, aboard Air Force One en route to Warsaw, as "an appropriate starting point" for negotiations.

President Carter, in his television interview Wednesday with four correspondents, was attempting to thread his way through this diplomatic quick-sand. But this is always a hazardous course for impromptu comment, and especially so at this extremely sensitive stage of Egyptian-Israeli negotiations, in the aftermath of the deflation of exaggerated expectations built up for the Sadat-Begin talks at Ismailia on Christmas Day.

It was evident to those familiar with the diplomatic complexities that Carter, in response to questions, wanted to commend both Sadat and Begin for their diplomatic initiatives, but wanted, especially, to nudge them forward to continued flexibility.

In the unstructured give-and-take of the interview, which followed Begin's public unveiling of Israel's peace offer earlier the same day. Carter repeatedly commended Begin for displaying "flexibility." That was intended, administration strategists stressed, to encourage more flexibility, not to pronounce an American benediction on the Israeli proposal.

But that is not the way many press accounts that flashed around the world interpreted the brunt of the Carter remarks. Carter was widely reported to have sided with, or to have supported, the Begin proposal, and to have opposed Sadat's call for an independent Palestinian state.

In Cairo, television reporters sought immediate comment from Sadat, who has made television interviews a fixture of what he calls his "electric shock" diplomacy.

Among those waiting to interview Sadat were two American television correspondents, Doreen Kays of ABC and John Sheahan of CBS.

ABC officials in New York said yesterday that they had immediately wired excerpts of Carter's remarks to correspondent Kays, who read them to Sadat after some preliminary questioning by CBS's Sheahan. The exchange between Sadat and Kays showed that the Egyptian leader reacted quite cautiously at first to Kay's questions, making no initial criticism of Carter:

Kays: "Can you reply to President Carter's statement last night at a news conference in which he said he did not support your demand for an independent Palestinian state?"

Sadat: "He did not support me? Very well, he may be taking a neutral position, but this is my view and I can't say at all that Carter has agreed with me about this no. To be fair, no. But this is my view since I met Carter last April and my view until this moment . . ."

Correspondent Kays, "she's a real tiger," one superior said proudly yesterday, pressed Sadat:

Kays: "Mr. President, President Carter also at his press conference last night, in not supporting your demand for an independent Palestinian state, did seem to side with Prime Minister Begin's peace plan . . . for limited-self-rule. Does this come as a surprise to you?"

Sadat: "For sure . . . I don't think anyone would oppose the world "self-determination." This is an appealing word. I don't know why Carter has done this but he has a right to have his own ideas like I have it and the Israelis have it. But let us hope that in the near future we can try and reach a solution."

Kays: "Perhaps its just a question of semantics, homeland . . . independent state."

Sadat: ". . . When I met my people yesterday through the television I could say there has been some step that has been adhieved after my visit to Jerusalem and the talks in Ismailia in the field of the Palestinian question. We are now differing or quarreling among each other in Israel and here in Egypt because they are speaking of some sort of autonomy or self-determination.

"This in itself is a great progress, a great leap, because 40 days before my visit to Jerusalem no one knew what would be the fate of the Palestinians. Begin and his government, the opposition and everyone in Israel used to say that this is an Israeli land that has been liberated. If after 40 days such a leap takes place and the differences between some sort of autonomy and self-determination, I consider this great progress and a great leap and very encouraging for the future."

Kays: "Aren't you disappointed by President Carter's latest statements?"

Sadat: "For sure I'm disappointed.For sure because I should like that we put all our efforts toward ending the suffering in this problem in the Middle East and giving the bright future for our next generation. This would take both of us some time, because we have to reopen the whole issue again."

Kays: "You were talking in terms of two months. You said that an agreement could be signed in two months. Do you now see that that has been delayed and could take much longer?"

Sadat: "It may be hindered for some time, but I think I can say that quoting '78 as the year of decision, I'm not exaggerating."

The Sheahan question-and-answer exchange with Sadat, which apparently followed, was broadcast by CBS on its evening news Thursday night in much briefer excerpt form, starting with a summation from Sheahan.

Sheahan: "President Sadat said he was surprised, disappointed and embarrassed by President Carter's public rejection of an independent state for the Palestinians."

Sadat was quoted as saying that "I don't know why Carter has done this. But he has the right to have his own ideas like I have it and the Israelis have it. But let us hope that in the near future, we can try and reach some solution to this."

Asked by Sheahan if Carter's statements "might make the job of negotiating more difficult?" Sadat said in part, "Well, for sure, it will make it more difficult for me because Carter himself is a dear friend, and he has my full trust . . ." but "he is making my job very difficult, Carter is."

Nevertheless, Sadat said, "We're not going to shuck the whole thing and say we'll go to war. No, we shall continue."

When asked "What bothered you most about the President's remarks?" Sadat said "what surprises me most" were the Carter comments on "the Palestinian question . . . the core anc crux of the whole problem" which Sadat said "embarrasses me.

Sheahan added in a concluding summary remark: "President Sadat has now revised his prediction of an agreement between Egypt and Israel within two months and blames the delay on President Carter"

These two TV interview segments were highly condensed, and further polarized, in press accounts transmitted around the world.

Media diplomacy, ironically, had come almost full cycle. It had been used dramatically by Sadat and Begin to come together; now it was displaying its other, divisive capacity as well.