Believer's baptism was reached twice, independently, by two movements that never met. In Zurich in January 1525, a small circle around Conrad Grebel concluded that Huldrych Zwingli's own reforming logic, that only what Scripture commands should stand in the church, ruled out infant baptism as an unwarranted medieval addition. On January 21, Grebel baptized George Blaurock, and Blaurock in turn baptized the others present, the first re-baptisms of what became the Radical Reformation. Their opponents called them Anabaptists, rebaptizers, a name meant as an insult that stuck as a description.
A full generation later and in a different country, the English Separatist John Smyth reached the identical conclusion by a separate route. Exiled in Amsterdam around 1609 and reading the New Testament congregations as gathered communities of professing believers, Smyth baptized himself and then his followers, founding what became the first English Baptist congregation. Thomas Helwys carried the practice back to England in 1612, and from that small exiled congregation the Baptist tradition grew into one of the largest Protestant families in the world.
That the same practice arose twice, on two separate readings of the same New Testament text and roughly eighty years apart, is central to how both traditions understand it: not a borrowed innovation but the plain conclusion any careful reader of Scripture is expected to reach.