Not always. I've witnessed thousands of entries for a non-existent "brand". I've seen almost 7,000 solution on one simple, but difficult brief. What gets so many people interested in participating? (I written on this topic before, and will continue to. It's worthy of more discussion I think). It's about the quality of the contest: is it inherently interesting; the prize; and if you're an "expert" how much down-time you have on your hands!
The crowd is not homogenous of course. Nor are the results. In fact, of the thousands of solutions in one particular contest ( I'll let you find it on your own!) I would suggest that over 50% are the same, or just variations on a theme. In this pool of creative there appear to be few experts and of the more professional solutions there are only a dozen or so that have real merit and are positioned thoughtfully with believable rationales.
All the same or different.
Experts and novices in the same crowd will give a wide ranges of solutions. If the contest is blind, there will be must less repetition. It's not that individuals will plagiarize on purpose, but sometimes seeing other solutions that they've actually thought about on their own tends to make people want to post it anyway. First come, first serve. Time stamps help. Traditionally, in an ad agency setting in the creative department, if you have a good idea it's best to blurt it out first!