Are we talking magazine stuff? If so, then both "exclusive" and "non-exclusive" deal with the concept of "First Rights." When you sell first rights (whether First North American, or First World, etc.) you're selling them the right to be the first to publish it in the location set. Usually, there's a time limit on the exclusivity--whether a month or six months or a year--from the time the issue hits the stands. Thereafter, rights in the work are relegated to "Reprints."
Non-exclusive means you can publish the short in more than one place at a time. There's no time limit before you can re-sell it. Generally, it's considered good manners to tell the others that it's been published, and you can't LATER sell exclusive rights to another publisher, even if the first publisher is non-exclusive. They will all have to be non-exclusive for it to work.
Now, if you're combining that with a BOOK, where first rights also exist, then there could be problems. See, the book publisher WILL want first rights. Sometimes, you can work with the contract paragraph dealing with "Second Rights" which is magazine work, and have the publisher allow the previous publication. In the case of exclusive rights, you couldn't enter into a book contract until after they expire. Often this is allowed when it's a well-known magazine, like Highlights for Children or such, because it's to the book publisher's benefit to have the exposure of the short. Parents will still buy it because there are pictures, which the Highlights story might not have (or they'll at least be different.)
Still, it's a question for an agent or a publishing attorney. They'll need to word the contract so that everybody plays fair. I wouldn't try to work it by yourself.
Good luck!
