Gregory Schnedinders, whose career as an aide to President Carter has had both high and low points, submitted his resignation yesterday as Carter's deputy assistant for communications.

Schneiders, who will leave the White House staff Septembber 14, submitted the resignation during a 20-minute meeting with the president and in a letter to Carter expressing "a deep sense of appreciation and affection."

In an interview, Schneiders said he plans to teach a siminar on the presidency at a Washington-area university he declined to identify, and to go into political consulting, including work for Carter's reelection campaign.

Senior presidential assistants were anxious to stress to reporters yesterday that Schneiders' unexpected decision to leave the White House now was not connected to the White House staff shakeup that Carter has ordered.

"Greg is leaving with good relations here," said White House chief of staff Hamilton Jordan. "It is not part of any shakeup."

Schneiders had been widely expected to leave the White House this fall and work for the Carter-Mondale campaign committee, probably as press secretary.Instead, he said yesterday he concluded recently that he "could put together a combination of things I'd enjloy doing and which could be lucrative" while retaining a connectiion with the Carter campaign as a party-time consultant.

He said he informed Jordan, White House press secretary Jody Powell and Gerald Rafshoon, Carter's media adviser, for whom Schneiders works, of his decision on Wednesday.

Rafshoon is expected to leave the White House in the fall to return to his advertising business and direct the and campaign in Carter's reelection effort. Sources said yesterday that the departures of Rafshoon and Schneiders are likely to mark the breakup of the so-called White House "image-making" operation created when Rafshoon joined the senior presidential staff last year.

Rafshoon is in charge of such White House functions as speech writing and television policy. When he leaves, these functions are likely to be dispersed to other parts of the White House operation and not remain consolidated under a new communications chief, the sources said.

Schneiders said he plans first to work with Robert Squier, a Washington political consultant who specializes in television production. Squier's clients include John Y. Brown, the Democratic candidate for governor of Kentucky, and William Winter, who is seeking the Democratic gubernatorial nomination in Mississippi.

After Raffshoon returns to his adverstising business, Schneiders is expected to work with him on the Carter Campaign.

Schneiders has many friends among Washington reporters and at times has been the subject of internal White House sniping as a possible source of news leaks. He said this had had nothing to do with his decision to resign, but conceded that he did not always enjoy working "in the constraints of a bureaucracy."

Schneiders' sometimes checkered career as an aide to Carter began in 1976 when the Georgetown University dropout and former Capitol Hill bar owner hooked up with the Carter campaign and became the future president's closest personal aide, traveling with him constantly.

After the election, it was widely assumed that Schneiders would be named Carter's appointments secretary, a job that would have continued to place him in close daily contact with the president. But then reports surfaced about financial problems in Schneiders' background, and, amid the unfavorable publicity, Carter awarded the job to Tim Kraft. Schneiders was relegated to a small basement office in the White House and placed in charge of reorganizing the government's disaster relief agencies.

However, when Rafshoon arrived at the White House he tapped Schneiers to be his deputy, a job that pays $48,500 a year and involves considerable influence over White House media policy.

Often irreverent with himself and other, including the president, Schneiders concluded his resignation letter to Carter with a Latin phrase he attributed to Gen. Joseph W. Stilwell -- "Illegitimati non carborundum." He said it translated "Don't let the bastards wear you down." CAPTION: Picture, Gregory Schneiders with Jimmy Carter in 1976, when Schneiders traveled constantly with the candidate. Bernard Gotfryd -- Newsweek