With regard to petrol engines ...
The Tritec (BMW/Chrysler collaboration) engine was used in 1st Gen models (hardtops built through November 2006 and convertibles built through July 2008). The Prince (BMW/PSA collaboration) engine was used in 2nd Gen models. A change was made to Prince engines effective with March 2010 builds.
The term "facelift" applies to mid-life changes made to each Generation.