The official Macross website describes the films as follows:
Macross Frontier: The False Songstress takes place in 2059 – following the near-destruction of the human race 50 years prior – and humankind has embarked upon an interstellar emigration project. The Macross Frontier fleet is on its way towards the center of the galaxy when it encounters a hostile alien species known as the Vajra. A concert by touring popstar Sheryl Nome becomes ground zero of an attack where both flight school trainee Alto Saotome and aspiring singer Ranka Lee are caught up in the chaos.
Macross Frontier: The Wings of Goodbye begins in the aftermath of the events of The False Songstress, when Sheryl Nome remains aboard the Macross Frontier as her health begins to rapidly deteriorate. Meanwhile, Ranka Lee has become a singing sensation in her own right, and prepares for her debut concert just as a joint military operation to hunt down the Vajra Queen gets underway.
After losing his VF-25 variable fighter as a result of the skirmish, Alto Saotome is hospitalized and the two songstresses, Sheryl and Ranka, rush to his side. Just as their love triangle is about to reach its climax, the architects behind the Vajra attacks are uncovered and Sheryl finds herself behind bars, accused of treason.
Macross Frontier began as the third TV anime series in the iconic Macross franchise, originally running from April to September 2008. The story follows trainee pilot Alto Saotome, aspiring pop singer Ranka Lee, and famed idol Sheryl Nome as they journey towards the center of the galaxy.