What is the difference between Existential and Religious Miracles?

A religious miracle is defined as a supernatural event that appears to break known and established scientific principles and laws, whereas;

An existential miracle is defined as an extremely fortunate event (or series of them) which, although very improbable, do not appear to be breaking any known scientific laws.

Examples of this would include people walking away unscathed from accidents, surviving under earthquake rubble or in mines and wells for weeks, and so on.

However, this division only seems to be present in Western sources and is not applicable to the Islamic definition of a miracle.

According to Ahl-us-Sunnah, a miracle (mu‘jizah) is an extraordinary phenomenon which Allah manifests on the hands of any of his prophets or messengers and in such a manner that mankind is incapable of reproducing it.

Indeed, there have occurred on hands of Allah’s prophets abundant miracles as to have established more than adequate proof to demand the intellect’s complete submission to what the prophets brought from Allaah – whether these occurred in response to their peoples’ requests or without and whether they were accompanied a challenge or not. In the Qur’an, miracles are called aayaat (sing. aayah) or signs.

As for a miracle being in conflict with the laws of nature or in harmony with them, this condition is found nowhere in the Qur’an, the authentic Hadeeth or the statements of the Salaf.[1]

And Allah knows best.

Reference:

[1] C.f. An-Nubuwwaat (1/165, 172 & 174), by Ibn Taymeeyah.