One way to define and classify miracles is by causality.
i) Providence is like an automated machine that does whatever it's programmed to do, nothing more and nothing less. Physical causes are unintelligent. Providence operates on the principle of internal causality. When nature operates as a closed system.
Providence is like a game of pool. The cue stick strikes the cue ball, which strikes the 8-ball, which rebounds against the cushion, in a series of unbroken cause and effect.
ii) Classical miracles bypass natural processes. At that point nature becomes an open system, subject to external agency. The miracle is causally discontinuous with antecedent states.
A classical miracle is like motion pictures. Motion pictures generate the illusion of causal continuity, but in reality, preceding and succeeding images are causally discontinuous with each other. In a classic miracle, there's a causal gap between the preceding chain of events and the miracle. The chain of events will resume after the miracle, because the miracle establishes a new antecedent state, and which point second causes kick in.
We might also compare classical miracles to body-swapping in science fiction. Transferring consciousness to a different body. Under that scenario, mind and body are discontinuous with each other inasmuch as that mind has no prior history with that body.
That has a real-world analogue with the resurrection of the body. On one model, God will create a duplicate body for the soul. It may be very similar to his former body, although this body will be immortal rather than mortal. But even if the new duplicate body was indistinguishable from his former body, his mind has no prior history with the new duplicate body. In that respect, it's like motion pictures.
iii) Coincidence miracles are in-between. They are like ordinary providence insofar as they utilize physical causes. They are causally continuous with the chain of events. Continuous with antecedent states.
But they are unlike ordinary providence inasmuch as they are more discriminating and specific. They reflect rational discretion. Both classical miracles and coincidence miracles involve an external agent who overrides the automatic setting.
A coincidence miracle is like loaded dice or stacked decks. It doesn't circumvent natural processes. But it requires the intelligent manipulation of natural processes by an agent outside the system.
BTW, "coincidence miracle" doesn't mean it's a coincidence. Rather, it means that independent chains of events coincide at that juncture, in a way that's too naturally improbable and opportune to be fortuitous.