No, they are not the same. Jerusalem artichokes, also known as root artichokes or sunchokes, are actually members of the sunflower family. The name Jerusalem is a mispronunciation of the Spanish girasol, meaning 'turn to the sun'. Globe artichokes are members of the thistle family.
The sharing of the name 'artichoke' refers to some similarity of flavor in these vegetables, but they have little in common beyond being pleasantly sweet.