“Pining away” is something one does when exhausted by emotional suffering. Like when you’re a dog, and your human goes to work without you. Or when you’re the heroine of a romance novel and your prince charming is called away by the king to go into battle against the bad guys. Nowadays it’s considered a little bit trite in many contexts, except when applied to animals.
It wasn’t always that way, though. “Pine” has quite a long history. It comes from Old English, and originally meant to suffer or endure pain. Except that “pain” didn’t exist back then (the word, I mean; presumably stuff still hurt). In spite of the obvious notion that “pain” is derived from “pine,” though, it isn’t.
There’s a story about the origin of “pining:” an unrequited lover can’t eat or sleep and eventually “pines away and dies” — and winds up in a “pine box” — and that’s why it’s called “pining.” It’s a good story, but it’s not where the word came from. It’s simply meant suffering ever since the Germanic origins of Old English.
“Pain,” on the other hand, didn’t originally mean suffering at all; it meant a penalty applied for some offense — it was often simply a fine. That sense is still around in the phrase “on pain of,” which you can easily find in legal documents. Not just legal papers though; “It was a warning..to refrain on pain of death” appears in Tarzan of the Apes and who knows how many other works of fiction.
“Pain” arrived in English in the 1300s, when it was borrowed from French. They used it only to mean penalties at first, just like the colonial government in Pennsylvania did: “Which Ordinances..shall be observed inviolably..under paynes therein to be expressed.”
“Pain” didn’t begin to mean physical suffering until the end of the 1500s. It might have been prompted by the famous Faerie Queene of 1590, which used it in the new way: “Loud he yelded for exceeding paine.” Since then, “pain” in common use has meant physical discomfort, and “pain” as a penalty has retreated further and further into legal jargon, usually in combinations like “on pain of…”. It’s close enough that most people don’t notice the distinction, and anyway, it’s pretty common to metaphorically refer to something like remitting a fine to “paying until it hurts”.
As for the older “pine”, its meaning never really changed, so unlike “pain,” which is probably pining away for its original meaning, “pine” isn’t feeling that pain at all.
