This is an often tricky area for newer writers, but it needn’t be. The answer is simple; if a publication states no simultaneous submissions, then don’t send them. Imagine the embarrassment of having them accepted in two places and having to retract them…What could your explanation be? “I completely ignored all your stipulations and did it anyway.” Might as well make a rude finger gesture and be done with it (and your reputation as a writer)!
In general, however, sending simultaneous submissions is fine; just have the courtesy to let the publication know. This happened to me recently; I sent the same two poems to The Ranfurly Review and Dogeater; in each case I stated they were simultaneous submissions. Ranfurly got there first and so I simply let Dogeater know and they were very polite with their reply that I received this morning. Simple!
I’d say competitions are completely different, however, and the same piece should never be submitted in competitions running at the same time. With prize money and a whole heap of time spent going through a mountain of submissions at stake – it’s a potentially toxic situation. Definitely wait until you hear a result before placing in another competition.