This is coming from an American, so this explanation is going to be a bit U.S.A.-centric:
The United States of America is federated under a central authority to facilitate cooperation, trade, and freedom of movement; this is why we call the central government the federal government. Canada, among others, is also federated.
Lemmy and the like are federated without a central authority, thus having no higher authority within this framework enforcing rules they must not infringe. Each member makes its own rules in its own territory, choosing whom they wish to federate or cooperate with. When moving to another member, or even non-member, like member states or territories, you need to move to a new address within the member you wish to join.
Countries such as the U.S.A., Canada, Mexico, and agreements such as the E.U. among others are federated within themselves; the ones mentioned also possess what are called federal governments.
This may be one of those things people where people may have at least some vague understanding of a concept but not the term for it.
A few definitions:
People, aside from the homeless, generally have an address in one or more countries, and remain under the authority of whichever country they happen to be living or traveling in. Likewise, people have — in this case, need — an address to interact here. Rather than get imprisoned in a country, a person simply gets banned from an instance. Like countries in the E.U., instances choose whether they want to continue to cooperate and stay within some agreement. A large difference between something like applications built on ActivityPub and the federation of countries, states, provinces, or territories mentioned above is the lack of a central federal government.
Rather than use Email as example, why don't we use federation amongst more familiar organizations as example? Why aren't we explaining Email like that?