There have been three American groups called “federalists”:
1) members of the Federalist Movement of the 1770s/’80s, who advocated strengthening the federal government;
2) members of the Federalist Party of 1792 and after, which was organized by Alexander Hamilton to advocate administration policy once he realized the Republican Party was doing the opposite; and
3) federalists who advocate the federal principle.
Generally, the upper-case “f” is used in connection with the first two of those groups and not with the other.
