Walking through an open-air Berlin market a day or so ago I discovered that the German word for pomegranate is Granatapfel. Seeing the apfel (meaning 'apple') part of the word suddenly made me realise for the first time that the 'pom' of pomegranate means 'apple' too (pomme in French). The OED also contains the obsolete forms granate-apple and pomegranate-apple for the same fruit.
Pomum was late Latin for 'apple' (malum was earlier Latin) and granate is ultimately from the Latin granum meaning grain or seed. French dropped the pomme connection and the modern French for (the) pomegranate is la grenade. It is because of the resemblance of explosive grenades to pomegranates that the metal shells got their name. The OED says that the deep red stone, garnet, is believed by some to have got its name because its colour resembled that of the pulp of the fruit pomegranate. Granate became garnet by a process of metathesis, which means that sounds swapped places. There are plenty of examples of this process happening in the history of English -- the Old English form of 'bird' was brid, and third and thirteen used to have the r before the vowel (as three still does) in Old English (þridda and þreotiene respectively).
Back to pomegranates and apples ... By coincidence, on the same day I was in the market, I also visited the Jewish Museum in Berlin. There is an exhibit, or installation, in the section devoted to early Jewish history, based around a pomegranate tree, and I learnt from the information given in the museum that some scholars believe that the 'apple' eaten by Adam and Eve in the Garden of Eden was, in fact, a pomegranate.