Old and New World Porcupines (Hystricidae and Erethizontidae families, respectively)
While all porcupines belong to the order Rodentia, Old World Porcupines (Hystricidae) and New World Porcupines (Erethizontidae) are actually not closely related to each other, and evolved their quills separately, in an instance of convergent evolution.
However, there are some similarities. All quills are modified guard-hairs, neither family “shoots” quills (though they are easily detached into skin if the quill-pig comes into contact with another animal), both families are herbivorous, and both families are among the longest-lived rodents (only naked mole-rats live longer).
There are some key differences, however, such as different dental formulas, very different skull shapes, and the largely arboreal (tree-dwelling) nature of the New World Porcupines, while the Old World Porcupines are terrestrial (ground-dwelling).
Images from Biodiversity Library on Flickr