My current area of research deals extensively with how models are related. When writing things down, I am constantly befuddled by the fact that there are two words referring to a situation where one thing is related to another: “relation” and “relationship”.

Now, I’m not a native speaker of English, but I do feel that there must be a difference in meaning here. Just to be clear: I’m referring to the words in the context of things (or even mathematical artefacts) being related, not people (where eg “relation” means belonging to a common family and “relationship” means social or romantic involvement) or other similarly social contexts.

So, looking around, the best explanation I could find was a forum post by someone going by the nickname “rightondev” at forum.wordreference.com. I copy it here for future reference:

Etymologically, a relationship concerns the sense of being related and thus does primarily apply to people. However, the concept of a relationship can be abstracted to all things, and results in the follow distinction between the two terms:

A relation is a concept relating two things.

A relationship is a conception of a relation.

Consequently, in many cases the distinction between the two words is unnecessary. In fact, unless a relationship supports added subtleties, the two words collapse for all intensive purpose to mean the same thing. Examples will make this clearer.

Example 1. Equality

In the case of 2=2, we can say that equality is both a relation and a relationship between the 2 and itself. The relation and relationship are the same because there are no addition ways to qualify equality.

Example 2. Greater than.

In the case of 3>1, the relation and relationship are distinct things. We should use relation when we mean to speak of the abstract concept of being more in number, but we should use relationship when we want to speak of the fact that 3 is precisely 2 more than 1. In this way, while 2 and 1 and 3 and 1 both relate by greater than, the exact relationships are distinct.

Example 3. Siblings.

In the case of two sisters, the word relation refers to their being siblings, but when it comes to the relationship between the two, the added subtlety of them being on good or bad terms can come into play. This is why we always choose to say “How’s their relationship?” when we want the gossipy details, but only say “What’s the relation?” when we want to find out how family members relate.

The second example is exactly what I’m looking for. In my ears, in modeling lingo this means:

A relationship is an instance of a relation.

In other words, I can for example specify the relation “Model Refinement” or “Diff” or “Naming Consistency” or “Architectural Connectivity” or whichever other kind of relationships I like. To do that, I can go on and describe a context in which it is applicable, define a notation for it, explicate its semantics, and so on. After I’ve defined a relation, I can identify particular relationships where it is instantiated.

For example, I can define the Operationalization relation that is applicable for requirements models and design models:

operationalization relation:  D × R

Then, for a particular setting, for a specific design model d1 and a specific requirements model r1, I can describe the Operationalization relationship between them:

d1 ——operationalization relationship——> r1