In another thread, there's a discussion of Redwing Blackbird, where it's noted that there are two entirely different songs by this name, one by Billy Edd Wheeler, one by David Francey.

Another Wheeler title, Coal Tattoo, was used a few years ago by a Sydney-area songwriter for an entirely different song she wrote.

There are two very different songs called The Foggy Dew.

I'm sure there are dozens (hundreds? thousands?) of other examples of pairs of songs with the same titles. Maybe it would be useful to collect as many as we can in this thread. Or maybe this has already been done, and someone will be kind enough to tell me where to look.