The following is CalQlata's understanding of these terms.
Let's begin with somebody that knew; Isaac Newton.
The title of his best known work; "Philosophiæ Naturalis Principia Mathematica" explains it perfectly.
These are its subjects:
Philosophiæ; the pre 18th century term for what we today refer to as science.
Naturalis; the natural behaviour of the elements.
Principia; the laws that govern natural behaviour.
Mathematica; the mathematical interpretation of these laws, what we today refer to as physics.
It reads today as the "mathematical laws of natural science".
A generic term that encompasses the study of nature.
The term includes the intrinsic behaviour, extinction, creation and evolution of [universal] inorganic and organic matter.
It does not include elemental activity that has been manipulated by intelligent species.
Therefore, we must limit the term natural to chemical and behavioural activity that has not been influenced by the human race.
For example; the experiments we perform in laboratories is not natural, it is artificial; its purpose is to exploit nature for profit.
Evolution as described by Charles Darwin and Alfred Russel Wallace is responsible for creating humans, just as it must be for all exploitative universal species. But as soon as a species gains sufficient intelligence to alter and control nature, further evolution on the planet(s) concerned is no longer natural.
Almost nothing that occurs on our own planet's surface has escaped the influence of humans, so very little of its future development can be considered natural.
The rules that define the behaviour of natural events.
These laws only apply to known, verifiable and actual matter and events.
The same laws apply to all levels of nature, from the smallest (atomic particles) to the largest (a 'Big-Bang').
Laws are not selective, nor are they open to interpretation or manipulation.
For example; rules that apply only to atoms or celestial bodies, or that are based upon statistics are not laws.
The prediction of natural characteristics or events using mathematics.
These are the mathematical formulas that may be used to predict the behaviour of all the elements; both individually and collectively.
The same mathematical formulas must apply equally to atoms and the planets and stars. They must also generate results that are verifiable by both observation and cross-referencing.
It must be concluded therefore, that as a minimum; the following:
relativity, quantum theory, anti-matter, sub-atomic particles, fusion in stars, uncertainty, event horizons, dark matter, black-holes, worm-holes (in space), folding universe, time travel, etc.
cannot be considered scientific, because they are not verifiable; either mathematically or perceptibly, and the mathematics used to define them are either statistical or manipulated.
You will find further reading on this subject in reference publications(69, 71 & 73)