WHEN THE SUBJECT of the lieutenant governor’s office comes up, there’s an old saw in Massachusetts political circles that is offered to explain its place in the state’s political firmament: There once was a woman who had two sons. One was lost at sea, the other became lieutenant governor, and neither was ever heard from again.

On the one hand, the job puts someone a heartbeat away from the governor’s office, and we’ve seen two lieutenant governors — Paul Cellucci and Jane Swift — take the reins as governor in recent years. But for the most part, those who’ve held the post toil in relative anonymity once you get outside the Beacon Hill bubble. For proof, watch what happened when then-Lt. Gov. — and great sport — Tim Murray did some first-hand survey research a few years ago in Boston’s Public Garden.

But that doesn’t mean the LG can’t play an important role in a governor’s administration. Two Democrats — Quentin Palfrey and Jimmy Tingle — are vying for the September 4 nomination for lieutenant governor. The winner will be paired with the victor in the party’s gubernatorial primary and go into the November match-up against the GOP ticket — widely expected to be led by Gov. Charlie Baker (who faces underdog challenger Scott Lively) and Lt. Gov. Karyn Polito (who is unopposed for the Republican nomination).

The two Democratic hopefuls, who came in for separate conversations on the Codcast, both bring a passion for the party’s values of tackling inequality, but with very different backgrounds.

Palfrey, an attorney who previously directed the health care division of the Massachusetts attorney general’s office and served as a senior advisor on jobs and competitiveness in the Obama White House, comes with deep public-sector experience steeped in public policy. Tingle,  known widely as a comedian who delivers humor with a progressive political punch, says he’s ready to bring a strong belief in Democratic Party values to public service.

Palfrey, who won the Democratic Party endorsement at its state convention this summer, said he’d like to serve as a “bridge between the governor’s office and cities and towns,” where he said lots of the things that most directly affect residents happen. “I think that this is a role that is what you make of it, and is what the governor lets you make of it,” said Palfrey, who referred repeatedly to the need to “lean in” on different problems facing the state.

Tingle also talked of serving as the administration’s liaison to local officials — a role that LGs, including Polito, have often been tasked with. But he said the principal issue he wants to be involved with is helping to tackle the state’s opioid crisis. Tingle tied that to his own recovery from alcoholism and the difference it made in his life when a man answering the phone at a Cambridge program he reached out to 31 years ago said, “You called the right place,” and got him admitted for treatment.

Both professed to be undaunted by the polling on Baker’s high favorability. They each argued that can change when the Democratic ticket brings its message focused on ways state government can address problems that have festered under Baker, from inadequate education funding to transportation woes, while highlighting the moderate Republican governor’s fundraising ties to conservative national Republican money.