Blaster Master Zero is an expanded remake of the original NES game, similar to how Metroid Zero Mission is an expanded remake of NES Metroid. Blaster Master Zero 2 is a new game, not a remake of any previously existing title, but I believe it has only been released on the Switch?
Blaster Master has a somewhat confusing history due to a couple of factors.
The first factor is that when the original game “MetaFight” was given a completely different story when it was brought to the West as “Blaster Master.” In Metafight, you play Kane, a soldier for NORA, piloting a first-of-its-kind tank named Metal Attacker, in a war against alien forces invading the planet Sophia III. In Blaster Master, you play an Earth kid named Jason, who finds an abandoned sci-fi tank in a cave near your house, which you pilot in a war against the evil Plutonium Army in your quest to find your escaped pet frog. The world of “Blaster Master” would be further expanded in the licensed English novelization, written by a person who received no guidance or assistance from publisher Sunsoft.
Side Note 1: The tank being called Sophia the 3rd in Blaster Master is the result of a mistake. In the NES game, the weapon equip screen displays the English text “SOFIA THE 3rd. NORA MA-01”. Sofia the 3rd (Sophia III) is the planet where the tank was designed. NORA is the organization that built the tank. MA-01 is Metal Attacker 01, the first Metal Attacker tank. People not knowing the story of Metafight (including the writer of the US novelization of Blaster Master) assumed Sofia the 3rd was itself the tank’s name.
The second factor is that Sunsoft really likes to release remakes of the first game.
Blaster Master: Enemy Below (Gamboy Color), Blaster Master: Overdrive (WiiWare), and Blaster Master Zero (3DS, Switch, PC) are all remakes of the original NES release. They are all different however, not only from the original but also from each other.
Blaster Master 2 (Genesis) is a Snake’s Revenge situation. Sunsoft decided to cash in on Western popularity by contracting a different team, with no input from the original creators, to create a sequel specifically for the Western markets. For Blaster Master 2, Sunsoft contracted British developers Software Creations. Blaster Master 2 is specifically a sequel to Blaster Master, not Metafight. Blaster Master 2 was not released in a Japan. While the game has some fans, it is largely considered to be mediocre.
Blaster Master Boy (aka Blaster Master Jr.) for the Gameboy is a Western rebranding of a Bomberman spin-off series called Bomber King. The first Bomber King was brought to the West as “Robo Warrior.” When Bomber King: Scenario 2 was being localized, Sunsoft apparently decided that Blaster Master was a stronger brand, and thus changed the main character’s sprite and rebranded the game as Blaster Master Boy.
Blaster Master: Blasting Again for the PS1 is a 3D sequel to Blaster Master specifically, not Metafight. Unlike Blaster Master 2, Blasting Again did see release in Japan, but that release was under the name “Blaster Master” rather than Metafight. Blasting Again draws its story in part from the licensed novelization of Blaster Master. At release, it was considered better than Blaster Master 2, but some considered that a relatively low hurdle to surpass. I’ve no idea how poorly it has aged.
Side Note 2: The English novelization of Blaster Master is a product of children’s educational book publisher Scholastic. Scholastic obtained the license to publish adaptations of multiple NES games, and did so under the “Worlds of Power” label. Ten titles were released, ranging from Blaster Master to Bases Loaded II. These books were written without any assistance from the game publishers and creators, and further alterations and allowances had to be made to fit Scholastic’s content restrictions. Cover art had weapons removed. References to death were removed. References to violence were downplayed or removed, and weapons were largely reduced to non-lethal attacks such as firing “stun rounds.” References to magic and the occult were downplayed or removed. To say that these adaptations were written with creative liberty is perhaps a bit kind.