Puddle, as a noun, refers to a small pool of water, usually small enough to walk through but not large enough for a raft.
What would a (temporary) pool of water larger than a puddle be called?
It just rained, so watch out for puddles
vs
It just rained quite a bit and there's a [large puddle] on the corner, so take the other road
I would imagine a pool of water might be correct, but I've never heard anyone refer to a body of standing rain water as a pool. And floodwater would be too much.
Best Answer
You've identified the best answer in your question: pool.
M-W:
Your example:
I've often heard people refer to "a large body of standing rainwater" as a pool. [emphasis added]