President Trump and special counsel Robert S. Mueller III. (Jabin Botsford; Win McNamee/The Washington Post; Getty Images)

The main protagonists of the Russia probe stayed largely out of public view on Monday. President Trump surfaced only late in the day for a White House trick-or-treating event, while special counsel Robert S. Mueller III was invisible apart from the signature he affixed to the indictment that was unsealed.

But their clashing dispositions — a contrast in the way they conduct themselves that goes beyond their competing approaches to legal combat — have become a palpable part of the investigation of Russian interference in American politics.

Trump has often treated the probe as a political assault to be met with counterattacks in both public and private, rather than a legal minefield to be navigated carefully. He has fired his former FBI director, lashed out frequently on social media, shuffled teams of lawyers and called for the prosecution of Democrats — all part of a highly public but so far unsuccessful attempt to derail the investigation.

Mueller, by contrast, has been silently methodical. He has not uttered a single word in public, works from an undisclosed location in Southwest Washington and demonstrated the same discipline and disdain for theatrics that defined his 12-year tenure as FBI director. Submarine-like in approach, Mueller has remained entirely below the surface except when delivering legal strikes that have included the raid of former Trump campaign chairman Paul Manafort's home and the indictments this week.

"Mueller is the opposite of Trump, the opposite of a showman, opposite of blustery," said Jack Goldsmith, who served as a senior Justice Department official in the George W. Bush administration. Mueller "is very quiet, very circumspect, very disciplined," Goldsmith said. "But he spoke very loudly and very powerfully" through the indictments of Manafort and his longtime business partner Rick Gates as well as the guilty plea of former Trump foreign policy adviser George Papadopoulos that were disclosed on Monday.

The president's defenders remain convinced he will be vindicated, and that Mueller's investigation will fail to find evidence that the Trump campaign colluded with Russia as part of a Kremlin interference campaign that, according to a report by U.S. intelligence agencies, sought to discredit the 2016 U.S. election and help propel Trump to victory.

"Here we are and it's November, 11 or 12 months into this thing, and still no evidence that Trump did anything," said Barry Bennett, a former campaign adviser to Trump. "I don't think Trump even sees [Mueller] as an adversary."

If Trump at times seems unconcerned with the extent to which his statements and actions complicate his legal position, Bennett said, it is because he sees himself as innocent and "doesn't even understand why we're engaged in this process."

One of Trump's lawyers, Ty Cobb, said Monday that Mueller's moves had "not been a cause of great agita or angst or activity at the White House."

But the statement was belied by Trump's own behavior, according to those close to him who said he spent much of Monday fuming over media coverage and venting to subordinates. He also lashed out in a series of posts on Twitter, saying Tuesday that the "Fake News is working overtime," and that Papadopoulos — an adviser Trump once praised as "an excellent guy" — was "proven to be a liar."

The predictably rapid leak of details about Trump's reaction from inside the White House only highlighted the contrast with Mueller, whose legal team has a lock on the progress of the probe. CNN reported on an indictment Friday night, but there were no reports that it was Manafort and Gates until just hours before it was unsealed. Nothing leaked on the plea and cooperation of Papadopoulos until Mueller chose to disclose it.

Mueller's refusal to engage publicly sets him apart from other legal and political adversaries that Trump has encountered since his entry into politics. Trump's combative impulses are often most effective when he can draw opponents into a public skirmish, whether on a crowded debate stage during the Republican primaries or in social media showdowns with members of his own party, including most recently Sen. Bob Corker (R-Tenn.)

Trump has, at times, sought to pressure key players in the Russia probe. He pressed former FBI director James B. Comey for an oath of loyalty before firing him in frustration as the inquiry expanded. More recently, Trump publicly berated Attorney General Jeff Sessions over his decision to recuse himself from matters related to the Russia probe, a decision that cleared the way for installing Mueller as special counsel.

Mueller has been protected from such entanglements, partly because of the nature of his job as special counsel — which, unlike leading the FBI, requires minimal interaction with the White House — but also because of his temperament.

Former associates of Mueller said his stealth approach reflects long-standing views of prosecutorial conduct, but also has the strategic advantage of unnerving targets of investigations, a list that may include Trump.

"The net effect of having these two powerful actions in court [Monday] combined with the mystery that has surrounded the investigation up until today has set everyone in Trump world on edge," said Matthew Miller, who served as Justice Department spokesman during the Obama administration.

Miller noted that other special prosecutors have taken a more public role. Kenneth Starr, who led the Whitewater investigation that culminated in impeachment charges against President Bill Clinton, spoke in public during the investigation and even appeared on news programs.

Mueller, by contrast, was not seen entering or leaving the courthouse on Monday. As the Manafort indictment was unsealed, there was no accompanying statement from Mueller's office describing the facts of the case — as is typical in Justice Department news releases — leaving reporters to read the extensive court filings to fill in the blanks. Even the location of his office in Southwest Washington is a mystery to many in government.

Mueller did meet with Trump earlier this year when Trump was interviewing candidates to replace Comey as head of the FBI, officials said. But within weeks Mueller was tapped as special counsel and is not known to have had any further contact with Trump since then.

Sari Horwitz, Devlin Barrett, Matt Zapotosky, Philip Rucker, Ashley Parker and Spencer Hsu contributed to this report.