It is logical, in a sense, that the names for a product and its producer are derived from the same source. That happens with the Armenian words for “honey” and “bee,” both having the same origin, *mel, a word that the reconstructed Proto-Indo-European language may have used to name both. Thus, we have մեղր (meghur “honey”) and մեղու (meghoo “bee”), with the suffixes -r and -oo added to the root megh, which should have sounded mel in Mesrop Mashtots’ times.
Both meghur and Latin mel (“honey; sweetness”), but also Greek mel (“honey; sweetness”), Irish milis (“sweet”), Old English mildeaw (“nectar”) and milisc (“honeyed, sweet”), and other words in Albanian, Old Irish, Old High German, and Gothic derive from Proto-Indo-European *mel-it (“honey”).
As you can see, while it is logical, it is not a rule that both words should have the same origin. Take English, where “honey” (Old English huniq) only appears in other Germanic languages (compare German Honig, derived also from a different Proto-Indo-European root, *khnónks. The same happens with “bee” (Old English bēo), also cognate with other Germanic languages (German Biene), which comes from a Proto-Indo-European root, *bhei (“bee”).
Meghur and meghoo have given us an interesting collection of compound words, such as մեղրալուսին (meghraloosin, “honeymoon”), մեղրահաց (meghrahats, “honey bread”), իշամեղու (eeshameghoo, “honeybee”).
There was another name for “honey” close to *mel in the Proto-Indo-European language, *med-hu, which yielded, among others, the English word “mead,” which designated a fermented honey drink in the Middle Ages.
That drink was also called “hydromel,” which leads us to show how Armenian and English have crossed their paths thanks to their common relative in the Indo-European galaxy, i.e. Latin. Other than the now exotic “hydromel,” the Latin word mel has come to be part of several common English words, such as “caramel” and “marmalade.”
“Caramel” comes from French caramel (“burnt sugar”), which is a loanword from Old Spanish caramel (caramelo in modern Spanish). The Spanish word possibly came from Medieval Latin cannamellis, an interesting combination of Latin canna (“cane”) + mellis (genitive of mel, “honey”).
“Marmalade” is related to quince, which is called marmelo in Portuguese and gave origin to marmelada (“quince jelly”), which was borrowed as marmelade and then “marmalade” in English. The Portuguese word marmelo derived from Latin melimelum (“sweet apple”), which originally designated an apple grafted onto quince. The buck does not stop here, for the Latin source was the Greek word melimelon, which combined meli “honey” and mēlon “apple” (yes, the source for English “melon”).
In the end, a warning for too quick translators: you may use endearing terms like “sweetie” or “honey” in colloquial language. In Armenian, you can say անուշս (anooshus), անուշիկս (anooshigus) as the equivalent of “sweetie,” but please don’t turn yourself into a laughingstock by saying մեղրս (meghrus) or something else to translate “honey.” Հոգիս (hokees. “my soul”) works perfectly fine.