it seems that maybe the FBI would deal with persons suspected or
believed to be criminals before they are brought before a federal
judge, first investigating them, then arresting them, then bringing
them before a judge, and federal marshals might deal with both civil
and criminal cases, perhaps more often the former, thus after the
matter is dealt with by a federal judge.
The primary duty of U.S. Marshals is to enforce court orders and carry out federal court warrants (including arrest warrants, search warrants, property seizure orders in civil and criminal cases, and not just post-conviction/post-judgment matters). They also sometimes provide court house security.
Thus, once an arrest warrant for someone is issued by a federal court, apprehending that person is within the scope of the U.S. Marshals, even though the U.S. Marshals wouldn't ordinarily be involved in the investigation leading up to the issuance of that arrest warrant.
But it is a little muddier than that. As federal law enforcement officers, they can also be called in to provide backup for other federal law enforcement agencies.
Also, keep in mind that many kinds of conduct are both state and federal offenses simultaneously, such as kidnapping and bank robbery.
In particular, the "Interstate Flight to Avoid Prosecution or Custody (Fugitive Felon Act)", 18 U.S. Code ยง 1073, makes it a federal crime to travel in interstate or foreign commerce to avoid prosecution, confinement after a felony conviction, or testifying in a felony case (even for persons convicted of felonies under state law).
According to its website, the U.S. Marshals service has the following duties:
The United States Marshals Service occupies a uniquely central
position in the federal justice system. It is the enforcement arm of
the federal courts and is involved in virtually every federal law
enforcement initiative.
The duties of the U.S. Marshals Service include protecting the federal
judiciary, apprehending federal fugitives, managing and selling seized
assets acquired by criminals through illegal activities, housing and
transporting federal prisoners and operating the Witness Security
Program.
Essentially the only investigation that U.S. Marshals routinely do is to locate individuals and sometimes property that is subject to seizure, in the course of carrying out court orders, and investigations related to their court security role (e.g. investigating potential threats to judges or their families).
The United States Marshals Service, Judicial Security Division handles this role, but the U.S. Marshals don't have exclusive jurisdiction over judicial and court security. For example, sometimes security for a court house will also be provided by less elite security guards hired by the General Services Administration (which provides security for all federally owned buildings), and sometimes threats to judges and their family will be investigated by the F.B.I. as well.
According to Wikipedia, the FBI's duties are as follows:
The Federal Bureau of Investigation (FBI) is the domestic intelligence
and security service of the United States and its principal federal
law enforcement agency. An agency of the United States Department of
Justice, the FBI is a member of the U.S. Intelligence Community and
reports to both the attorney general and the director of national
intelligence. A leading American counterterrorism,
counterintelligence, and criminal investigative organization, the FBI
has jurisdiction over violations of more than 200 categories of
federal crimes.
Although many of the FBI's functions are unique, its activities in
support of national security are comparable to those of the British
MI5 and NCA, the New Zealand GCSB and the Russian FSB. Unlike the
Central Intelligence Agency (CIA), which has no law enforcement
authority and is focused on intelligence collection abroad, the FBI is
primarily a domestic agency, maintaining 56 field offices in major
cities throughout the United States, and more than 400 resident
agencies in smaller cities and areas across the nation. At an FBI
field office, a senior-level FBI officer concurrently serves as the
representative of the director of national intelligence.
Despite its domestic focus, the FBI also maintains a significant
international footprint, operating 60 Legal Attache (LEGAT) offices
and 15 sub-offices in U.S. embassies and consulates across the globe.
These foreign offices exist primarily for the purpose of coordination
with foreign security services and do not usually conduct unilateral
operations in the host countries. The FBI can and does at times carry
out secret activities overseas, just as the CIA has a limited domestic
function. These activities generally require coordination across
government agencies.
The FBI was established in 1908 as the Bureau of Investigation, the
BOI or BI for short. Its name was changed to the Federal Bureau of
Investigation (FBI) in 1935. The FBI headquarters is the J. Edgar
Hoover Building in Washington, D.C. The FBI has a list of the top 10
most wanted fugitives. . . .
Mission
The mission of the FBI is to "protect the American people and uphold
the Constitution of the United States".
Priorities
Currently, the FBI's top priorities are:
- Protect the United States from terrorist attacks
- Protect the United States against foreign intelligence operations, espionage, and cyber operations
- Combat significant cybercriminal activity
- Combat public corruption at all levels
- Protect civil rights
- Combat transnational criminal enterprises
- Combat major white-collar crime
- Combat significant violent crime