HELSINKI, SEPT. 9 -- In past summits with American presidents, Soviet President Mikhail Gorbachev often came with a surprise. Today he came with a cartoon.

In comic-book colors, the cartoon depicted Bush and Gorbachev as boxers in shorts and shirts. A referee with a globe for a head stood between them, holding up their arms in mutual triumph. A battered, melting figure labeled "Cold War" lay in the foreground. The word "knockout" was written in Russian at the bottom.

"That's wonderful!" a smiling Bush exclaimed as Gorbachev presented him with the framed cartoon.

Symbols are a big part of modern summitry, and the Soviet drawing seemed to capture the spirit as the two men began their third meeting and the two nations, once bitter rivals, continued their rapid pace toward more normal relations. Envisioned by Bush as an opportunity to have a frank discussion of the Persian Gulf crisis, aides likened it in some ways to the kind of meetings Bush holds with allied leaders.

Not that the two see the world in precisely the same way. Their joint press conference this afternoon in Finlandia Hall revealed clear differences in their approach to the crisis, a reminder that while both men seem determined to continue on the path of improved relations, they are still mindful of their own interests.

But the public body language was all positive: relaxed, friendly and at times even playful.

"I don't know if I would be allowed to tell you a secret here," Gorbachev began one answer. "I haven't asked President Bush if he'll let me. But I must admit that I'm dying to take the risk and tell you."

As the audience of journalists and aides to the two leaders laughed, Bush turned toward Gorbachev, shifted in his chair and sat in mock anticipation.

At another moment, Bush was struggling with his earphone, used to listen to the simultaneous translation. Thinking the problem was with his microphone, he banged on it. "It's not working," he said.

"Hit it again," Gorbachev told him.

Asked whether today's meeting had deepened their sense of mutual trust, they turned toward one another, each motioning cheerfully for the other to go first.

Bush said he believed their relationship had steadily improved, citing the storm-tossed Malta summit last December and their Washington summit in June, particularly the relaxed day they spent at Camp David, as the catalysts.

"Neither of us when we talk try to hide our differences," Bush said. "Neither of us try to indicate that we look at exactly every problem the same way. But the very fact we can talk with the degree of frankness without rancor, I think, enhances mutual understanding."

The friendliness displayed here today represents a long step from the depiction of Gorbachev as a "drugstore cowboy," which was the way White House press secretary Marlin Fitzwater described him in the spring of 1989. That was before Bush, who relies on personal relationships with world leaders to help guide his actions, got to know the Soviet leader better.

But it was Gorbachev who identified the real change that brought the two men together for consultations on the gulf rather than negotiations over arms control: "History dictates that a lot is going to depend on whether the two countries can work together. That is not our ambition, it's just the way history has gone."

The meeting began on schedule, with Bush arriving first at the Presidential Palace, the Finnish official residence, which sits on a public square at the edge of the Gulf of Finland.

A formal arrival ceremony was held in the palace's Yellow Salon, whose polished parquet floors carry the 1872 imprint of a Russian craftsman. As aides opened tall, double doors to the balcony, Bush and Gorbachev entered from opposite ends of the room, Bush smiling broadly. "How are you, sir?" he asked. Gorbachev greeted him warmly, then pulled out the cartoon for the president's approval.

After a wave from the balcony, the morning session began, running more than 2 1/2 hours, with only note takers and translators present.

National security adviser Brent Scowcroft, who has been at the center of management of U.S. policy on the Persian Gulf, took notes for Bush. Secretary of State James A. Baker III and Soviet Foreign Minister Eduard Shevardnadze met in a separate room.

At a photo session before lunch, reporters shouted questions, and Bush seemed to delight in their inability to elicit useful responses. At one point, while Gorbachev replied in Russian to a question, Bush looked at American reporters standing blankly along the wall and joked, "You heard what the man said."

Lunch was followed by a two-hour meeting between Bush and Gorbachev assisted by a number of aides. While the details of the meetings were not immediately known, officials said they were characterized more by broad discussions than by sharp exchanges on details of gulf policy.

"Differences still remain," Bush said at the press conference. "But the common ground, in my view, surges ahead of these differences."