I don't know. This point and quatona's cause me to sit back and think.
But I think the above I just posted applies: given that miracles are specific interventions, whereas laws are what they are by definition because of induction, I don't think you can use the former to define the latter.
As for distinguishing, that comes down to the subjectivity of coincidence, which of course isn't compelling by any real standard other than personal experience: I experience something really strange and very coincidental, therefore God might be involved. Actually, coincidence senses like this are probably how we assume any intelligence is involved. But you do have miracle moments that are pretty obvious in that they very clearly involve breaking the laws of nature (the former example is more implicit and subtle), where, you know, God parts the sea and stuff.