statistical use of "relation" vs "relationship" When describing statistical models such as regression outputs, both terms the relation and relationship seem to be often used interchangeably. Examples include


*

*Summaries of papers in Wasserstein et al. 2019 including "...an observed relationship..." and "..local descriptions of relations between models and the obtained data...". 

*Harrell's 2010 useR tutorial uses "relationships" and his blog uses both terms in the same post (e.g., Road Map for Choosing Between Statistical Modeling and Machine Learning.


As an example with a simple linear regression with predictor variable $x$, response variable $y$, slope variable $b$, and intercept $a$, $y \sim a + b x$, how would one describe the results?

$b$ describes the linear relationship between $x$ and $y$?

or 

$b$ describes the linear relation between $x$ and $y$?

I understand both terms have slightly different terms in common English (e.g,. this post on english.stackeschange.com, but have not been able to find statistical definitions for the two terms. Is the use of the two terms nuanced across sub-fields? 
 A: The following isn't with respect to technical statistical usage, but it does represent one informed opinion about how best to report results of statistical analysis.
A Senior Copy Editor at a well respected journal once complained about the use of the word "relations" in a manuscript my colleagues and I had written:

The term “relations” is not the standard terminology. When referring to HRs [hazard ratios], we prefer the wording: “relationship between X and Y”, “association between X and Y”, or “X is associated with Y”, etc.

I have since endeavored to conform to that Editor's recommendations. As different journals can have different style sheets governing their copy editing, I make no claim that this distinction is universally expected or accepted.
A: Those words do not have specific statistical meaning, same meaning as in plain English applies in here. The words are used interchangeably, at least I never noticed anyone using them in different contexts, to mean different things. Usually in scientific literature when someone uses a word in some specific meaning, the definition is given in advance, so that the term is not ambiguous, e.g. "the relationship ..., such that...", or "the relationship defined as...".
