Federal and state governments are the two main levels of government in the United States. Here’s the difference between them:
The federal government is the national level government run out of Washington, D.C. The President, Congress, Supreme Court of the United States, all of those entities are part of the federal government. Think of it as an umbrella that covers the whole nation.
State-level governments are run by each individual state. They have similar parts to the federal government, such as a Senate, House of Representatives, a court system, etc. The laws that state governments make are only applicable in that state, though.
The U.S. Constitution (basically the rule book for our U.S. governments) dictates what powers the state and federal governments have. For example, only the federal government can regulate interstate commerce. That makes sense, because such commerce involves multiple states by definition. State-level governments have tried to intervene in this (and other federal areas) before, for example during the Grange Movement.
While studying U.S. history you will encounter many instances of state and federal (and even local-level) governments interacting, so it’s important that you understand the difference between the two main levels of government.