Jack Smith, the special counsel investigating former President Donald J. Trump, has brought a streamlined case against Mr. Trump, accusing him of attempting to subvert democracy. This effort aims to move the case to trial quickly in a presidential election year.

On the other hand, Fani T. Willis, the district attorney in Fulton County, Ga., has taken a different approach in prosecuting Mr. Trump for his attempts to overturn the 2020 election results. She has indicted 18 co-defendants and the former president, a strategy that critics argue will take a much longer time.

However, Ms. Willis has surprised both the Trump team and some Justice Department officials with her swift actions. She has obtained plea deals from three lawyers connected to Mr. Trump within one week: Kenneth Chesebro, Sidney Powell, and Jenna Ellis.

These developments are undoubtedly good news for Mr. Smith, but they also present logistical and legal challenges as Mr. Smith and Ms. Willis simultaneously work to hold Mr. Trump accountable. Defense lawyers and former federal prosecutors acknowledge the complexities involved.

Despite Mr. Trump’s attempts to delay the federal election case until after the 2024 election, the trial is still scheduled for March. However, because of the plea agreements and the possibility of more co-defendants striking deals, it is now uncertain when the Georgia trial will begin, leading to increased uncertainty surrounding both cases.

Here is what you should know about the impact of the plea deals on the federal case:

Can evidence from defendants in Georgia be used against Mr. Trump in his federal trial?

Yes, but it’s complicated. Any publicly released documents or statements, including court appearances by Fulton County defendants, can be admissible as evidence in the federal trial.

It is unlikely that Mr. Trump’s Georgia trial will take place before the federal case, given the initial timetable set by Ms. Willis’s team and the recent activity driven by demands for a speedy trial from Ms. Powell and Mr. Chesebro. Consequently, any public testimony against Mr. Trump would likely come after Mr. Smith has already presented his case.

Ms. Willis has the discretion to decide whether she will share material not entered into the official record with Mr. Smith’s team. Therefore, federal prosecutors often prefer to proceed first when faced with dual-track local prosecutions to avoid deferring to district attorneys elected by voters.

The best-case scenario for Mr. Smith is if Fulton County prosecutors provide interview transcripts to the federal government. In that case, the special counsel’s office could subpoena the defendants or other witnesses, asking them under oath if their previous statements were truthful. Cooperation with local prosecutors tends to translate to cooperation with federal prosecutors.

However, Ms. Willis might request information sharing from Mr. Smith’s team, which could pose issues. The judge overseeing the federal election case has imposed a protective order that restricts sharing evidence with non-parties, and federal prosecutors are obligated to keep grand jury testimony confidential. They can request its sharing with local prosecutors, but this is a rare occurrence.

Are Ms. Willis and Mr. Smith coordinating their efforts?

Contact between the two prosecutors has been minimal, according to sources familiar with the situation. Ms. Willis emphasized her prosecutorial independence before charging Mr. Trump, expressing that she doesn’t even know who Jack Smith is.

However, the recent plea deals could change this situation, although Ms. Willis’s team still emphasizes their independence. The Justice Department allows interactions with other offices and encourages early cooperation to avoid conflicts and duplications of effort.

Whatever evidence Mr. Smith obtains from Georgia will be shared with the Trump defense team during the discovery process.

Can defendants who cooperate with Ms. Willis assert the Fifth Amendment right against self-incrimination in federal court?

Yes, but the protection may be limited. If Mr. Smith subpoenas Mr. Chesebro, Ms. Powell, and Ms. Ellis as witnesses against Mr. Trump, they can refuse to testify based on their Fifth Amendment rights, even if they effectively waived those rights in Georgia.

However, Mr. Smith can respond by bringing federal charges against them, giving him the same leverage that Fulton County prosecutors had during the plea negotiations. Any admissions made on the stand in Fulton County could potentially be used against them by Mr. Smith. Ms. Powell and Mr. Chesebro are already believed to be two of the unnamed co-conspirators in Mr. Smith’s federal indictment.

Is there a downside for federal prosecutors?

Possibly. Indicting a former president and prosecuting him for similar crimes in two jurisdictions is unprecedented. The Justice Department typically tries to avoid concurrent cases to prevent discrepancies in witness testimony that can undermine the entire case.

Mr. Trump has a habit of discrediting potential witnesses and co-defendants, which prompted the judge in his federal case to impose a limited gag order. His legal team will likely focus on weaknesses and discrepancies in the testimony.

Former prosecutors note that the Fulton County indictments, based on Georgia’s broad anti-racketeering law, pose challenges similar to other complex cases involving testimony from former allies who have a history of making false statements.

The plea deals are undoubtedly positive news for Mr. Smith and Ms. Willis, but they present challenges for Mr. Trump.

Contributors Richard Fausset, Alan Feuer, and Danny Hakim have contributed reporting to this article.