Though their similar spellings may lead to these two words being easily confused, they have quite different meanings.
The root of writhing is writhe, a verb that originates in Old English as wriðan (or writhan), meaning “to twist or bend.” That meaning has carried down into the modern day as perhaps the most commonly known definition of writhe: “to twist the body about, or squirm, as if in pain, violent effort, etc.”
Willow couldn’t hold back the moan as the dark magic flowed into her, easing the ache that had filled her with Tara’s loss. The magic showed her everything she could do now with just a thought, how she could make Warren writhe in agony, torturing him without a touch.
Another commonly used definition of writhe is “to suffer acutely from embarrassment, revulsion, etc.” This kind of writhing may or may not have a physical movement accompanying it.
Remembering when she’d tried to end the world never failed to make Willow’s soul writhe at all the evil things she’d done.
While hopefully your characters aren’t squirming in pain or embarrassment while they’re having sex, it’s possible they’re twisting or bending with pleasure (or effort), hence the often-seen writhing in sex scenes.
While it has the same letters as writhe, wither, the root of withering, is a very different word altogether. It stems from the Middle English word wydderen, which means “dry up, shrivel.” Again, that definition has followed the word down through the years, as “shrivel; fade; decay” is the primary meaning of wither.
Jack quickly discovered that, for all that the former Commodore was a pirate himself now—he sailed on a pirate ship under a pirate captain, which, by the proper application of logic, would make anyone a pirate, even ex-Naval officers fallen from grace—Norrington still had a deplorably low opinion of the breed. “He imagines us so foul that flowers wither as we walk past, I’m sure,” Jack muttered.
Other definitions of wither follow a similar theme, as most of them have to do with loss, e.g., of moisture or youth. My own favorite definition of wither is “to abash, especially with a scornful look.”
Norrington was no better at cook’s assistant than he was at scrubbing decks, and Jack began to fear that the man would slip some poison into his drink one night. He glared at Norrington, who quickly looked away. Jack thought he’d done well to cow the former Commodore, having been on the receiving end of the other man’s withering glare more than once and knowing it to be a fearsome thing indeed. Then he realized that Norrington had turned away to hide his laughter.
To bring it back to those steamy bedroom scenes, the only things that should be withering are the rose petals strewn liberally about. If someone is withering, in all likelihood that means his or her partner has been replaced with some supernatural creature who wants to suck out all their moisture.
If you want to remember which is which, it might be helpful to note that wither and shrivel are synonyms and have the same short vowel sound (as in “it”). Writhe has the long vowel sound as in “violent,” which might bring to mind the “violent effort” definition.
Dictionary.com – here and here
Online Etymology Dictionary – here and here