Your stated premise suggests a fair bit of federal and state/local agencies jurisdictional overlap.
At the federal level, primary investigative responsibility is typically allocated to agencies per specific expertise in enumerated crimes; however, investigations almost always reveal other criminal activity that may seem to fall under another agency's purview. In those cases, the original agency may continue as the lead and cooperate with other concerned agencies (think ad hoc task force)--or not, dependent upon circumstances and prosecutorial guidance.
At some point there will be federal/state jurisdictional overlap (i.e.; an enumerated federal crime may also be a state crime). In these cases of concurrent jurisdiction, state and federal agencies may conduct separate/independent investigations, and at some point share results; or they may coordinate their investigations, up to and including working cohesively as a task force (state/local investigators may, as circumstances warrant, be specially deputized to bestow federal investigative authority).
Understand that in cases of concurrent jurisdiction, the criminal violation may be prosecuted (trials held) in both state and federal courts. Concurrent jurisdiction does not constitute double jeopardy. Upon convictions sentences may be set to run concurrently or consecutively (twenty years in a federal prison must be completed before the sentenced person is turned over to the state to begin a twenty-year sentence imposed by the state).
