They are nothing alike and are not interchangable. I don't know why the name is the way it is. There do appear to be at least two types of artichokes. Champlain and Marc Lescarbot returned to France in 1607 and seem to have brought the vegetable back with them. Now the Jerusalem part is much more interesting.
Unqualified artichokes are green and thistly-looking, and are, well, artichokes.
They are green and consist of overlapping scales. Jerusalem artichokes are tubers which are cream colored and similar in appearance to a skinless extremely knotty potato. So a cardoon recipe would be quite different from a modern artichoke recipe. When you cut a cardoon the stalk will string like a stalk of old celery or peel down like a stalk of rhubarb.