‘Why can’t they work together more?’: In Rome, Healey and Wu partner on tackling climate change. At home, not as much.

But beneath the unity and the gauzy rhetoric spun from within a villa nestled in Vatican City are two leaders who have different visions for the best way to tackle the existential crisis that is climate change for our waterfront state, where vulnerable neighborhoods flood on sunny days and where the water line in Boston Harbor will likely rise as much as 7 inches this decade.

While both City Hall and the governor’s office have declared climate change a major priority, Healey and her administration have not embraced all of Wu’s big swings, such as her ongoing push for free and improved transit, citing the reality of the T’s tight operating budget.

Healey’s administration has instead leaned harder into working to attract climate technology businesses and boost the state’s green energy workforce.

In Rome, Healey’s drive to find climate solutions that boost the state’s economic competitiveness was on view as she pitched business leaders and consultants on bringing their companies to Massachusetts and used the world’s stage to announce a brand-new loan program, funded by private philanthropic dollars, to jump-start the careers of future train operators, heat pump installers, and wind turbine technicians back home.

Wu, meanwhile, kept her focus on the steps municipal leaders can take closer to the ground to enable cities to adapt to — and protect against — the worst consequences of a warming planet, rallying mayors from around the world to follow some of the bold actions she’s spearheaded in Boston, such as allowing residents to opt in to power their homes or businesses with “cleaner, locally sourced electricity.”

When asked about the tenor of her relationship with Wu, Healey said in an interview that while “others might” feel that the two leaders are competitive, in reality, they share “an urgency and a desire and a recognition that this is a big deal.”

“[Climate change] is hurting a lot of people,” she said.

The three-day summit hosted at the Vatican gathered nearly 100 leaders representing more than a dozen countries inside a converted villa to take in lessons on responding to a warming planet and to hear Pope Francis’ call to “heed the cry of the earth.”

Massachusetts had an outsize presence, with emissaries such as top brass from the University of Massachusetts, big names in research and administration from MIT and Harvard, and heavyweights including Timothy Sweeney, the CEO of Liberty Mutual, and deep-pocketed Boston philanthropists James and Cathleen Stone.

“There is an enormous consensus here that Boston and the Commonwealth are offering a general framework that the whole world can learn from,” said UMass Boston Chancellor Marcelo Suárez-Orozco, one of the co-organizers of the summit.

In Rome, Wu betrayed some of her frustrations with the constraints of City Hall when she got a chance to engage with one of her top climate priorities: improving public transit. In a meeting with Rome’s mayor, which the Globe was invited to observe, she explained to him that while the city is in charge of the streets, the state is in charge of the MBTA.

Rome, on the other hand, controls its own public transit system, which consists of metro, buses, and trams. Mayor Roberto Gualtieri said he could understand how it feels to be a mayor who ultimately has less power than higher authorities who influence the city’s fate.

“It’s a fractured system,” Wu said.

The MBTA, much of which serves those who live or work in Boston, is a division of the state’s Massachusetts Department of Transportation and therefore operates under the state’s purview.

It means city officials need the state’s buy-in if Boston wants to make some of its bus lines or other transit free, dedicate new bus lanes, or install new infrastructure — all proposals Wu has pursued as means to curb emissions by getting more cars off the roads.

And while the T’s general manager and the state’s transit secretary have been “amazing partners,” Wu said, the city remains hamstrung when it comes to pushing for more transit access, among other climate-related priorities.

“I look with envy upon other cities [that] can just decide where they need to add new stations or stops,” Wu said in an interview at the Vatican. “We have a lot of arbitrary-feeling lines that get drawn across municipal boundaries.”

The state has thrown up obstacles to Wu’s climate goals in other areas, too. Wu had been ecstatic about the possibility of joining a state pilot program to ban fossil fuels in new construction — the only way for Massachusetts communities to take this step without violating state regulations. State lawmakers said at the time that the inspiration for some of the language in the program came from then-candidate Wu’s Green New Deal for Boston.

Wu said at the time that state officials gave her “clear indications that Boston would not be chosen,” and that the Legislature wrote the law in such a way to effectively bar Boston from the program.

Ultimately, Wu pulled back from the state’s pilot program and blamed the state for her decision.

“It was frustrating from the beginning,” Wu recalled in an interview at the Vatican. “The program was never designed for us and in fact, was explicitly designed hoping, planning, for us not to be in it.”

Instead, the city moved ahead with more scaled-back goals, including an ordinance that requires large buildings to slowly reduce emissions over time and adopting a “stretch code” that sets energy efficiency requirements for new construction and major renovations.

A spokesperson for the Executive Office of Energy and Environmental Affairs said the office will “continue to collaborate” with Boston to “reduce greenhouse gas emissions and adapt to a changing climate.”

To be sure, Boston has made some advances: embracing infrastructure upgrades, helping residents and businesses move to renewable energy, and providing young people with job training in those industries, for example.

The city has invested money in environmentally friendly funds, and propped up a utility program that allows residents to opt in to powering their homes or businesses with “cleaner, locally sourced electricity.”

Talking to a reporter about Wu’s climate goals, London Mayor Sadiq Khan, who chairs an international group of nearly 100 climate-focused city leaders, including Wu, argued that mayors move faster than any other leaders when it comes to reducing emissions.

“Mayors are doers. National governments are delayers,” Khan said. “Michelle is a good example of that.”

Kannan Thiruvengadam, executive director of Boston’s Eastie Farm, said on some issues, such as building emissions and investments in the MBTA, “it does feel like the city wants one thing and the state wants another.”

Thiruvengadam said he was pleased to see Healey and Wu stand together in Italy, but said his East Boston community would have “more confidence and faith” with tangible results from the summit such as a proclamation or new program that would directly benefit the neighborhood. East Boston is a so-called environmental justice neighborhood, where the population on average is low-income, has a high percentage of people of color, or where a sizable number of households do not speak English very well, if at all. These communities are more at risk of being unable to participate in decision-making on environmental issues or gain access to environmental resources.

“At home, a couple may quarrel, but when they go out, they try to be together. I don’t see a problem there,” he said. “The deeper questions do come up, though. Why can’t they work together more?”

Hessann Farooqi leads the advocacy group Boston Climate Action Network, which has worked with the Wu administration to push a series of climate policies. He said he was proud to hear some of the city’s biggest accomplishments championed on an international stage, and that he has been pleased to see Healey introduce investments in the climate workforce.

That said, he hopes to see those promises translate into action back in Massachusetts.

“We have got to do it here at home,” he said, noting the urgency for Healey’s push for more public transit funding and resiliency initiatives as the end of the Legislature’s session approaches. “The proof will be in the commitments they make. ... If inspiration came through the summit, then great. Let’s get to work.”

Samantha J. Gross can be reached at samantha.gross@globe.com. Follow her @samanthajgross.