Stanley Smith Stevens described 4 kinds of scale based on different approaches to measurement and the comparisons and inferences that can be drawn. The 4 are:
Nominal: Items can be sorted into named categories (named – hence nominal). These categories should generally be MECE. Items are sorted into one category. People of one nationality can be French, German, Italian etc by citizenship. I can’t be more French than you are French or than you are German.
Ordinal: All items can be consistently ranked in order against some criteria. (Ordering is not always possible. A situation is ‘intransitive’ if A>B and B>C does not imply A>C. See intransitive decision making)
Interval: Not only can be ranked but the position on the scale can be meaningfully represented and the gap between items has significance. Note that an interval scale cannot be intransitive .
Rational: Not only can be ranked and positioned but the relative positioning to an accepted fixed point is meaningful.
Six metres is three times longer than two meters is still arguably a commentary about an interval scale but the orbit of Earth is X times the diameter of the orbit of Mercury is arguably a commentary on a rational scale, as there is an accepted fixed point.
On an ordinal scale, the melting points of mercury, water and iron are in that order.
On the Celsius interval scale, boiling point of water is 100 degrees hotter than freezing point of water.
On a rational scale (such as degrees Kelvin), boiling point of water is approx. 36.6% hotter than the freezing point of water.