In combining forces on climate change, these two men have sought to present themselves as a high-profile team in opposition to President Trump on this issue. On Tuesday, Mr. Brown and Mr. Bloomberg announced they would lead a group of states, cities and businesses in pledging to adhere to standards set by the Paris climate pact — after Mr. Trump announced that the United States would withdraw from the agreement.

In truth, these two men are not as dissimilar as they might appear. Mr. Brown is 79; Mr. Bloomberg is 75. Both can be, shall we say, irascible. And both won considerable support by being viewed as something of a free spirit: playing by some rules of politics, while happily flounting others. Mr. Bloomberg, who doesn’t exactly fit the profile of what most people might consider a Republican, left the party to become an independent as he thought about running for president.

“It’s an interesting character study,” said Kevin Sheekey, Mr. Bloomberg’s top political adviser. “One guy is Jerry Brown — a California leftist. The other is the global king of capitalism. That doesn’t make sense. But when you think about it they are remarkably similar and their success has come from their similarities.”

Might this cross-country lineup make a difference? Well, at the very least two big names from the two coasts guarantees that what might otherwise have been just another news release gets a bit of notice. That is no small matter in these hectic days.

“They have a remarkable power to coordinate U.S. forces — business, environmental, state, local, corporate — in a way no two other individuals could,” Mr. Sheekey said. “That really is the game at this point.”