Theology plays a part in the separation and sometimes synonymous meanings of Paranormal and Supernatural.
Paranormal: Normally means beyond what science can currently explain. Normally was used for the Magic terminology found in the occult.
Supernatural: Beyond the laws of nature, physics, science, reason and logic etc. Supernatural normally mean beyond all human explanations of something normally a miracle of God.
Overtime they started to merge with the synonymous definition of beyond science. Inshort.
Preternatural: While has more than one type of meaning, with the birth of modern science, it meaning outside the natural course of events but not associated with witchcraft or demons. Considered fake miracles that were associated once by demons, gods, or God. So they removed those components and was left natural.
Paranormal: Was used to explain something normally when science couldn't explain something happened beyond reason, aka magic.
Supernatural: Was used to explain the works beyond, all science aka human understanding and magic. But that is also when Magic was associated with demons to consider Magic an illicit method. However modern years has started to undemon Magic terminology and definitions to explain both miracles and magic under the supernatural definition as simply beyond science and nature.
Something to consider when you make new categories.