pine

As a tree, pine traces from Old English *pīne back to Latin pīnus. As a verb meaning to waste away with longing, it comes from Old English *pīne ("pain"), from Proto-West Germanic *pīnā ("pain, torment, torture"), possibly ultimately from Latin poena and Greek ποινή, meaning punishment or bloodmoney.

The tree-name and the pain-word arrived in English by separate paths but converged on the same spelling. The verb pinian ("to torment") settled into the sense of pining — a slow, aching longing, a gentler descendant of torment.

Pine (the ache) is a cognate of pain, both descending from the same Proto-West Germanic root for suffering and torture.