Gerry Conway wrote the first appearance of Man-Thing, complete with origin story. ("Savage Tales #1," cover-dated May 1971.)
Len Wein wrote the first appearance of Swamp Thing, complete with origin story. ("House of Secrets #92, cover-dated July 1971.)
When you boil the plots down to the bare essentials, you find the origin stories had some points in common. ("Sincere young scientist is being persecuted by bad guys, and accidentally ends up being transformed into a terrifying muck-monster which is called some sort of 'Thing'. . . all of which is only slightly better (if at all) than it would have been for him to die a quick, clean death . . .")
Both guys had, I gather, handed in their respective scripts long before either comic book emerged from the pipeline to be printed and distributed to the public.
Conway and Wein were, literally, roommates at the time they wrote those stories.
But as I've heard it: Each man swears he didn't discuss the details of the relevant script with his buddy before those comic books were published (one at Marvel and one at DC). And neither man has ever accused the other of spying on him, reading his notes, and then plagiarizing him by hastily dashing off a similar script for a rival company! They both seem to think it's a funny quirk of fate, rather than anything that requires a conspiracy theory to explain!
If both of them are convinced that it was all a coincidence and that nobody was victimized, who are we to say we know better? We weren't hanging out in their apartment at the time, were we? They ought to know more about what was going on, and about each other's moral fiber, than we do!
As ArnoldoAAD suggested, it's quite likely that they were both inspired by the same old comic book character -- "The Heap" -- who had a long run in the Golden Age and continued to be used, off and on with variations, in later stories from more than one company.