The federal government has power over issues that affect the entire nation. However, the powers granted to the federal government must be spelled out in the Constitution or ruled "necessary and proper" as interpretations of the Constitution by the Supreme Court.
Powers that only the federal government has include declaring war on other nations, printing money, establishing and supporting military forces such as the Army and Navy, regulating international and interstate trade, and running and funding the postal system. All of these powers are either directly listed in the Constitution or have been interpreted as constitutional by the Supreme Court.
The federal government shares some powers with states. The concurrent powers help the state and federal governments work together yet function independently from each other. These powers include collecting taxes, making and enforcing laws, building roads, borrowing money, setting up court systems, and spending revenue for the welfare of the general population. The Constitution allows the federal government these powers, and allows the states the same powers.
While the federal government can regulate trade between states, it can't regulate trade within a state's borders. The federal taxes are different from the state taxes, because the Constitution allows it to be so. The federal government's powers are limited by the Constitution, while the states' powers are limited only by what is forbidden by the Constitution.