Armed Fighbird is formed from the Armed Combination of Fighbird and the Flame Breaster. In the anime, he is only referred to as "Fighbird".
When neccessary, Fighbird will summon the Flame Breaster by sending a signal orb into the sky. The Flame Breaster will then combine and form the front skirt, chest and head armor for Fighbird, thus completing Armed Fighbird. This is Yuutarou Katori's main combat mecha for the first half of the series. Armed Fighbird can transform into his jet mode with the Flame Breaster docked, so technically he still has an alternate mode.
In order to combine with Jet Granbird to form Great Fighbird, however, both robots will have to ditch their support units (the Flame Breaster and Breaster Jet respectively). However, the Flame Breaster can still merge with the Flame Sword and become Great Fighbird's main weapon while the Breaster Jet can become Great Fighbird's shield.
During Fighbird's first battle, his power proved to be unequal to Draias' monster, so he summoned in the Flame Breaster and combined into Armed Fighbird, dispatching the monster shortly thereafter.