As Ms. Guadagno has darted around the state, still focused largely on her plan to relieve the property tax burden on voters, she has also unveiled a new platform: ethics.

Promising to “bring a new era of ethics and transparency to the State House,” Ms. Guadagno, in rolling out her plan recently, used the opportunity to attack Mr. Murphy for not releasing his tax returns and for allowing his running mate, Sheila Oliver, to run for lieutenant governor and an Assembly seat at the same time.

Even as she promises to improve the conduct of elected officials, Ms. Guadagno is still a member of the Christie administration, which was enveloped by the George Washington Bridge scandal that led to a former top aide and an appointee of Mr. Christie being convicted of corruption. Ms. Guadagno was never implicated in the scandal.

The election of the next executive in Trenton, the state capitol, isn’t even the state’s biggest political story — that would be the federal bribery trial of New Jersey’s senior Democratic senator, Robert Menendez, which could have implications that reverberate far beyond the state.

Against that backdrop, both candidates have been campaigning with the larger story lines in mind. Outside the federal courthouse here where Mr. Menendez’s trial is taking place, Ms. Guadagno’s campaign workers handed out packs of M&M’s candies, with a note attached saying “M&M’s: Murphy and Menendez” that attacked Mr. Murphy for refusing to say whether Mr. Menendez should resign if he is convicted. Mr. Menendez has denied any wrongdoing in his case.

Mr. Murphy, as he did throughout the primary, regularly cites Mr. Trump in his stump speeches and at town hall meetings. He promises to stand up to the White House “with a steel backbone” and often tethers Ms. Guadagno to the president, despite her chilly attitude toward Mr. Trump.

And he has offered policy positions related to high-profile national issues, including saying he would “exhaust all legal means, including suing the president” to counter Mr. Trump’s decision to end a program that shielded young undocumented immigrants from deportation and assuring such immigrants that they would have a haven in New Jersey.