Both unitary and federal government systems can be defined by the relationship between the national government, representing the nation as a whole, and any subnational governments, representing subnational divisions like states or provinces. For example, within the United States of America, the national government is on the level of the nation itself, while each state maintains its own subnational or state-level government.
Within unitary systems, such as the United Kingdom, the national government is supreme, and the majority of power is centralized within it. The national government delegates powers down to the subnational governments, which then exercise these delegated powers and implement policy decisions that originate within the national government.
Federal systems, such as the United States, tend to have a weaker national government, with powers distributed among the national and subnational levels. This can sometimes lead to conflicts among jurisdictions. Consider the status of medicinal or recreational marijuana in the United States: it is legalized or decriminalized in a number of states while still remaining illegal on a federal level.
In both systems, there is a great degree of variability in exactly how power is distributed. The United States was originally designed to have a weaker national government with more autonomous states, but, over the course of its history, the national government has consolidated more power.
All that said, both systems are quite different in how they distribute power and execute matters of policy and law. In terms of similarity, it may only be possible to say that both systems are ways to administer a nation. Ultimately, the unitary/federal split is chiefly concerned with how power is distributed. How the government is formed, how laws are made, how administrations change—all of this is largely removed from the simple question of how power is distributed among administrative divisions.