I don't understand the question really. If they are two separate poems, going to two separate markets, through two separate publishers, what's the issue? I see no moral or ethical delima involved. And there certainly isn't a legal one even if it were to the same publisher. They have the choice of accepting or rejecting, and deciding if it is too similar.
But since you asked...
Let's say you have a poem about a kid and a ball. Well, if the only difference were the color of the ball in the two poems then yes, they're the same poem and you'd be lazy for trying to get milage out if the same work.
But if the kid is different and the ball is different, and the town and circumstances are different, if the "road traveled" is different, even though the outcome or result is the same, t's still a different poem. We all have similar experiences but travel different paths to get there. I mean we all may get up in the morning, go to work, and wind up at home that night, which would make for the same "kind" of story, but each would be fairly different I would guess. And if you (as one person) were telling these different stories, you get credit for taking the time and effort to make each one there own.
Better yet, let's say you do a series of poems about a particular tree in you yard or nearby park. You may talk about it one way when you were there with your love, and another when you were there with your kids, or still another when you were there by yourself just naval gazing one day.
Or, pin it down even finer. The same tree, the same day, different people and different times of the day, and you write about how the tree looks, how the others "use" the tree, how the light plays upon it. Same tree, same day, same story "only the names are changed to..."
Though yours deals with a particular adventure of one individual (you), I see nothing fraudulent in writting for two different audiences or telling that story from two different viewpoints. Comics, Screen Writers, Hollywood in general, do it all the time. Look at the sitcom, done to death in "different" versions yet each almost as popular as the last. Or for that matter, look at only one show, Law and Order, one of the most popular shows on tv and it has told the same story over and over many times in different ways. What's even worse (considering tv) is that in the older episodes an actor is a criminal, now, in the newer shows, they're lawyers or judges.
People change words or story flow, or bits and pieces all the time based on the audience. An audience of doctors is LIKELY to appreciate something different, while the average reader may appreciate the humor involved in some light hospital and doctor bashing, or particular calamity you experienced.
I think about the famous John Grisham. He puts a lot into his books and every one seems different yet the same. Basically it's a form that is followed and the specifics are changed to suit the story. It's a person or group involved in the legal practice, a murder or some other crime, research and detecting, a trial (sometimes), and an outcome that usually has what would be called a happy ending but lives changed forever. It's always the same but always different. Nicholas Sparks is kind of the same.
Here, you're admittedly telling the SAME story to two different audiences. Well, don't people ALWAYS consider their audience when relating something? Would anyone write for say a medcal journal the same as they would for Apple Valley or Mytholog? Would you tell a 25 year old secretary about your car problems the same way you would tell your mechanic? No, but you might want tell them both the same story nonetheless.
I think the worst that would come up is that those who were privy to both might accuse you of trying to get extra milage from a single poem, but how many is that really likely to be? And if we're going to start applying strict standards to poetry in these terms, we'd all better learn a new way to talk about trees, love, etc. or never write about the same tree twice.
