It's an information structure and presentation question. The first constituent is typically topic, and the second one is focus:
(The) kids are at school. (as opposed to somewhere else)
There are kids at school. (as opposed to, say, adults, or no one at all)
Like Darius has said, with questions, they become the following:
Are the kids at school? (as opposed to somewhere else)
Are there kids at school? (as opposed to someone else)
It's a bit confusing, as the は/が distinction also has to do with the same information structure stuff. Certainly the first one needs は instead of が to really work right. However, since は is a topic particle, it almost always goes in the topic slot - it can only go in the focus slot if you're comparing things:
The kids are at school, but the adults aren't.
*学校に子供はいる。 is ungrammatical outside of this context, as far as I know.
Basically, the topic slot is for old information (things that are already being talked about) and the focus slot is for new and/or contrastive information (things that are just being mentioned, or things that are being compared). With questions, this works out to the second (focus) slot being filled with what's directly being questioned - so, in the first example, it's where the kids are that's in question; and in the second, it's who is at school that's in question.