You cannot compare apples with oranges, but of course, you can compare an orange and a նարինջ (narinch), because both refer to the juicy fruit used to make your everyday breakfast beverage and both have the same origin. And, as we will see, apples were somehow part of the origins of the English orange.
Oranges probably originated in Southeast Asia, and were already cultivated in China around 2500 B.C. However, the ultimate origin of both English orange and Armenian narinch (pronounced narinj in Classical Armenian) is India. The fruit was called naranga, which means “orange tree,” in the Vedas, the sacred books of Indian religion written in Sanskrit, although the origin of the word is unknown. It seems to come from a non-Indo-European language of the Indian peninsula, such as Telugu, Malalayam, or Tamil.
The fruit went from India to Western Asia with the Arabs as intermediaries. Along went the name: it remained as narang in Persian, turned naranj in Arabic (Arabic does not have a g), and became narinj in Kurdish and Armenian. According to German linguist Heinrich Hubschmann and his disciple Hrachia Adjarian, the Armenian word originated from Persian narang.
The fruit went to Europe through Portuguese travelers to China, and through Arabs. It received the name of “Chinese apple” in some languages: they are called sinaasappel in Dutch and appelsin in Low German, literally “China’s apple” (hence Russian апельсин apelsin “orange,” which you may hear sometimes in Eastern Armenian). Interestingly, “Chinese apple” is the name of the pomegranate in British English.
Interestingly, Spanish and Portuguese most probably adopted the word through Arabic influence in the Iberian Peninsula (Spanish naranja and Portuguese laranja), but Portugal helped spread the word to Southern Europe and the Middle East: Greek πορτοκάλι (portokáli) and Turkish portakal. Believe it or not, Arabs today call the fruit burtuqāl برتقال; the word nerinj is used for a different citric.
The name and the fruit reached England through a more indirect path. Old Italian borrowed the word from Arabic and turned it into melarancia (mela + (n)arancia “apple of orange”). The French calqued the word from the Italians and turned it into pome orenge (“apple of orange”). Finally, Old English borrowed orenge/orange from Old French, without the “apple” part. (In the end, the French dropped the word “apple” too.) And this is how English orange sounds quite close to Armenian narinch, only with the vowel o at the beginning.
There is one difference, though: orange in English means both the fruit and the tree. In Armenian, we have two different words, although close enough: narinch for the fruit and նարնջենի (narncheni) for the tree. The suffix eni is equivalent to the English “-tree,” as in khntzoreni “apple tree.”