While there were two others known as Manhunters from Mars, such as T'Omm J'onzz who once visited Earth-One and Roh Kar who once visited Earth-Two, the standard bearer for that name was J'Onn J'onzz who would become the Martian Manhunter. As a charter member of Earth-One's Justice League, J'Onn had carved a niche for himself as a protector of the Denver metropolitan area of that era in the suburb of Middleton. Adopting the alter ego of police detective John Jones, the Manhunter used his various abilities to protect his adopted world. To that end, he was accompanied on several adventures by the dimensional travelling fellow alien known as Zook.
On Earth-Two, J'onzz's counterpart was physical education teacher and chemist Thomas "Tex" N. Thomas. Discovering with his prized pupil Daniel Dunbar a secret formula that turned them into positive and negation receptacles of atomic power, the pair of "Human Handgrenades" known as TNT and Dan the Dyna-Mite were born. They themselves were the primary protectors of their own world's Denver metropolitan area. Although not tied to the Mars of his universe, his fellow atomic All-Star the Atom had visited Mars and possessed superhuman abilities on par with J'Onn, which Tex likewise would've displayed on that world!
While both pairs of green and blue clad protectors possessed superhuman strength and physiques as well as awesome energy abilities that they could emit through their eyes or hands, respectively, J'Onn and TNT were also displaced from their native worlds and both aliens of Earth-One. This occurred for TNT and Dyna-Mite in the mid-1940's when they were sent via Per Degaton's time traveling ship to that world from their own just prior to J'onzz arriving there himself. Zook himself was also from a parallel planet in an adjacent dimension. And on a couple of occasions, J'onn would travel to TNT's native Earth-Two in teamups with his League and their dopplegangers in the Justice Society of America.
Meanwhile, J'onzz as first police detective John Jones and then later as the Martian Manhunter decided to assimilate into humanity and provide it protection. In his civilian identity, Jones began a partnership with police woman Diane Meade whose Earth-Two twin was socialite Joan Carter. Joan was the former fiancee of scientist Robert Crane, who's humanity ended when his mind was placed in the body of Robotman following his body's death.
Eventually, J'Onn left Earth-One for a new world in hyperspace for the fugitive Martians of Mars-One while Zook apparently returned to his native dimension. TNT and Dan after decades of confinement in an underground bunker eventually moved into Kandor and Atlantis, respectively. Later, TNT moved with the Kryptonians of Kandor to their new world Roykyn in another universe.
Prior to leaving Eath-One, J'Onn assumed another identity after his John Jones alias was presumed deceased, that of international playboy Marco Xavier. Secretly a subcontractor for the villainous organization known as VULTURE, when Xavier seemingly perished his alter ego was assumed by the Manhunter, in order to bring it down along with its mysterious leader Mister Vulture. Turns out, Faceless was the original Xavier. On Earth-Two, Marco's doppleganger was also wealthy playboy in Tex Thomson, who after a series of international adventures worked first for the local government in an American city as Mister America, then overseas in Axis controlled Europe as the covert double agent known as Americommando. A master of disguise, Tex was able to assume the identity of numerous German officers, while secretly undermining its influence with his alter ego. Using a specialized cape that enable him to fly, Mister America had a lengthy career on the side of justice... like the Martian Marco but unlike his actual counterpart in Mister Vulture/Marco... and was a member of the All-Star Squadron alongside TNT as well as allied with his sidekick Fatman who somewhat resembled Xavier's costumed identity.