However even within the same type rating you may have additional training or restrictions. For instance the FAA prohibited Southwest from using the same pilots across three generations of 737 (Classic, NG, MAX), so Southwest ditched the Classics when they bought the MAX.
A big advantage Airbus has is their more modern designs are full fly-by-wire, so they're able to more practically compensate for the handling characteristics in software.
As far as I know (not a pilot or aeronautics engineer) MCAS was more or less an attempt to do the same to a non-fly-by-wire plane, and we see how that turned out...
The picture is just to show how far the plane has deviated from its original design on a colinear (e.g. same price/size target among the new generation) scale. If you want more depth into the pains Boeing goes to not trigger a "new design" recertification, there are plenty of articles on it released during the initial Boeing MAX MCAS forced crashed saga, such as ArsTechnica's series of articles.
The Airbus A330 and A350 share the same type rating. (At least some variants; I'm not an expert.)