The United States constitution was the main construction source that preserves the formal separation of powers. Both the federal and state governments draw their authority and powers as defined by the Constitution. There are clear responsibilities and governing powers contained in there.
The layer-cake federalism or the dual federalism and divided sovereignty is a political framework where responsibilities and power are shared between those of the state and the federal government. These responsibilities and power sharing are clearly defined for execution by either body without interfering with the affairs of each other.