Man-Thing first appeared in Savage Tales #1 (May 1971), written by Gerry Conway with art by Gray Morrow.
Swamp Thing first appeared in House of Secrets #92 (June-July 1971), written by Len Wein with art by Bernie Wrightson.
So, since they are both similar in appearance, and since they both live in the swamp, you would think that perhaps that one of them is inspired by the other, but this is not so, according to the writers (note that editor Roy Thomas is also credited with inventing Man-Thing, along with Conway and Morrow).
From a nice interview here, here is Len Wein on the topic:
One of which is that I was rooming with Gerry Conway who wrote the first Man-Thing story. It was just independent creation. We were doing Swamp Thing and Gerry and I think Gray Morrow was doing Man-Thing. Neither of us knew the other was doing the same thing. The weirdest aspect is that I actually wrote the second Man-Thing story; the whole "Whatever knows fear burns at the Man-Thing's touch". In Gerry's first story anything the Man-Thing touched burned. It was a protagonist who could never interact with anybody so I came up with the idea of fear.
So they did not take the idea from each other.
However, it is very likely that both men drew their inspiration from the same source, which is the classic 1940s character, The Heap.
The Heap, drawn by Mort Leav and written by Harry Stein, was a popular comic book by Hillman Periodicals during the 1940s.
He is basically the same concept as both Man-Thing and Swamp Thing, and was actually revived for a comic book the SAME YEAR as Man-Thing and Swamp Thing (after the fact, though).
So it is quite likely that this character existing during the Golden Age is the explanation for how two men both managed to come up with the same idea without taking it from each other, they were both just influenced by a THIRD character.
That's it for this week!
Feel free to suggest urban legends you'd like to see debunked (or confirmed) in a future installment!