Rhûn was the Elvish word for 'east', and so the wide region known as 'Rhûn' covered a great range of eastern lands. Out of those lands came Easterlings, broadly known as Men of Rhûn, who belonged to many different cultures. All of those cultures, so far as is known, lived under the shadow of the Dark Lord.
The eastern lands of Middle-earth were little travelled and little known, but some of the eastern tribes made war against the western lands, and so their names, at least, were recorded in western histories. Most famous among these were the Wainriders, who warred against Gondor for nearly a century, and the Balchoth, who were defeated by Eorl at the Battle of the Field of Celebrant.
Even after the Fall of Sauron at the end of the Third Age, resistance still remained among the Men of Rhûn, and there are records of the soldiers of Gondor and Rohan travelling far into the east of Middle-earth to battle against their remaining enemies among the Easterlings.
In the Third Age, the terms 'Men of Rhûn' and 'Easterlings' were used interchangeably. It's not entirely clear whether this equivalence also applied to the Easterlings of the First Age, but it does seem that they at least came from beyond Eriador, so the title probably applies.
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