Answer
Supernatural is a subcategory of paranormal. Supernatural relates to the existence of something beyond the visible observable universe. Paranormal is anything not scientifically explainable.
For example, ghosts are not scientifically explainable (yet), therefore they are paranormal. An invisible ghost would be supernatural (in addition to paranormal) because it cannot be seen or observed in our universe. A visible ghost would only be paranormal because it can be seen in our universe.
Explanation
According to Merriam-Webster, America’s most trusted dictionary, the definition of paranormal and supernatural are as follows:
Paranormal – not scientifically explainable
Supernatural – of or relating to an order of existence beyond the visible observable universe
Paranormal is a very broad term. Anything not scientifically explainable is paranormal. Therefore, before scientists could explain electricity it was paranormal.
Supernatural is a more specific term. Anything in existence that cannot be seen or observed is supernatural.
We cannot see wind, but it can be observed and measured. Atoms are invisible to the naked eye, but can be seen microscopically.
As of yet, ghosts cannot be scientifically explained, which classifies them as paranormal. Ghosts can also be supernatural if they cannot be seen. But, ghosts that can be seen are only paranormal.
But, can ghosts be observed? A difficult question to answer, but no. Not everyone has been in their presence or noticed them, which makes them hard to observe.
Anyone can see a ghost, but are more apt to see one in an altered state of consciousness, such as being fatigued and/or stressed. Though, not all ghosts can be seen. Some may not appear, but influence objects instead.
Sources:
https://www.merriam-webster.com/dictionary/supernatural
https://www.merriam-webster.com/dictionary/paranormal
https://www.thesun.co.uk/news/4051536/reasons-why-people-see-ghosts-paranormal-activity-experts/
The Paranormal Report 