To clarify, in the original Gundam series, the Zeon "Zaku" was the first mobile suit built, and it was decisively winning the war for them. Earth started a crash program to counter the threat, designing three mobile suits to counter the Zaku. GunCannon, GunTank, and GunDam. Tank proved to be kind of shitty, and Cannon was too overspecialized for long-range bombardment. RX-78 Gundam, however, proved to be a multirole powerhouse that not only rendered the Zaku into cannon fodder, but had an edge over the many, many specialized Zeon MS designs purely due to the ease of reconfiguring it for a different mission. The Gundam was used as the basis for the less capable mass-produced GM suit, and exact duplicates (along with minor variants) of the prototype were also built.
Fast forward to Zeta, and Earth's newest prototype is designated the "Gundam Mark II." Other than a similar design aesthetic, the name seems to be more of an homage to the famous original, in the same way that the A-10 is the "Thunderbolt II" and the F-35 is the "Lightning II" (named after the war-winning P-47 and P-38 fighters of WWII). Roughly halfway through the series, the lead builds a new suit using the Mk. II as a base (along with features from other AEUG suits), resulting in what he named the "Zeta Gundam."
In this chronology, "Gundam" is simply an "honor" designation given to the first suit of a new generation, much as the flagship of Starfleet in Star Trek is always "NCC-1701 USS Enterprise." I don't recall the word "Gundanium" ever being mentioned in the UC timeline, and a cursory check shows it to only exist in the "After Colony" timeline of Gundam Wing.