President Ronald Reagan and President Daniel Ortega at last have something in common: They are making bad trips.

The big difference between Reagan's journey to a Nazi cemetery and Ortega's mission to Moscow is that Reagan's is morally indefensible while Ortega's is merely politically destructive. Neither of them had the wit to cancel.

Reagan has put his friendship with Helmut Kohl, the chancellor of West Germany, above his friendship with his own people, many of whom, especially Jews and World War II veterans, are deeply offended by the idea of an American president visiting graves of German war dead that include Hitler's infamous elite, the SS.

In Managua recently, Ortega told Democratic Sens. Tom Harkin (Iowa) and John Kerry (Mass.) that he was going to Moscow to get a $200 million loan for seed and fertilizer -- the U.S. blocked his request to the Inter-American Development Bank. In keeping his schedule, he has profoundly embarrassed those members of Congress who refused to approve Reagan's request for new aid to Nicaragua's "contras."

Reagan says, in refusing to change his plans to visit the Bitburg cemnetery, that he does not wish to "cave in."

Something of the same macho spirit seems to be impelling Ortega, who took off for Moscow two days after the House vote on contra aid. He didn't even say thank you, although he had told Rep. Edward J. Markey (D-Mass.) that he would feel "morally obligated" to make a "reciprocal gesture" if Congress came through for him.

Let's say Nicaragua has a right to be "nonaligned" and that its leaders can go where they please. Let us further concede that the trip was long-planned and that Ortega, desperate for cash, has to get it where he can. Reagan at least has the excuse that the German Bundestag has emphatically voted in favor of the Bitburg visit. Ortega cannot argue that Soviet leader Mikhail Gorbachev would be incensed if he put off his visit. Gorbachev has shown distinct coolness to becoming deeply involved with Nicaragua.

But even if Ortega insisted on going, he could have redeemed the trip somewhat by announcing at planeside, that, by the way, he was going to lift press censorship. But Ortega has shown again that he can be most relied on to play into Reagan's hands.

Senate Republican leader Robert J. Dole (Kan.) went on television to say that Ortega's itinerary was "proof positive" that Congress had erred, and called for economic sanctions. Sen. Jim Sasser (D-Tenn.) said he would have voted differently if he had known that Ortega's first response would be to take wing for Red Square.

Reagan has been urged by 82 senators to skip Bitburg. No matter what he says at the site, the most eloquent indictment of Nazism will not change his being there. If he inveighs against the "Master Race," he will erode his rationale, which was to lift the burden of guilt from the Germans.

He has been unable to grasp that the visit was like a depth charge exploding in the memories of death-camp survivors and World War II GIs. The Jews fear the onset of revisionism, a resurgence of the denial that says, "It wasn't 6 million, it was only 2 million ." Already the anti-Semites are coming out of the woodwork. The German magazine Quick said the uproar showed once again "legendary Jewish power."

On Sunday, his chief of staff, Donald T. Regan, represented the president as being "wounded" by the controversy. Reagan had sufficiently recovered by yesterday, however, to complain that the news media was to blame, for worrying the controversy, like a dog worrying a bone.

Prominent Jews invited to join the traveling party all declined. In a declaration of moral bankruptcy, the White House wheeled out former president Richard M. Nixon in the guise of St. Christopher, the patron saint of travelers. He blessed the trip.

Some Democrats like to think that the outcry contributed to Reagan's defeat on the contras; the Reagan spell has been broken. But it was probably Vietnam more than Bitburg that worked against him. The 10th anniversay of the fall of Saigon occasioned a spate of bitter images: children playing in the wreckage of B52s, American POWs bowing to their captors. It was enough to dampen ardor for "behavior modification" in another small, poor country.

Case-hardened Reagan-watchers note that he has come back from more serious, although less emotionally charged, disasters.

Ortega may pay the piper for his insensitivity sooner. With his help, Reagan may be able to engineer a reversal on aid to the contras.

Both of them need new travel agents.