Does English have frequently used ordinary words that distinguish between equality and equivalence?

Does English have frequently used ordinary words that distinguish between equality and equivalence?

For example:

It was the same man on the photo.

Equality. The two persons are identical.

She ordered the same dish as her cousin.

Equivalence. The two dishes are the same kind of food, but they are two objects.

Solution 1:

Interesting question.

There really aren't any common words that express the difference between equality and equivalence. Wearing the same hat, eating the same food, driving the same car — all of these things point to equivalence rather than equality or identity.

What the hat, food and car represent here are instances of classes, but not the same instances. To express that one instance of car is identical to another instance — for example, that you and I were driving the same Ford Fusion, California License Plate No. FOOBAR1 (sorry if that is a real plate number), on the same day, I in the morning and you in the afternoon — we would have to go out of our way to express that by actually citing the plate number or explaining that I loaned you my car or you loaned me yours.

Even to say we were driving the identical car would not cause the listener, at first, to suspect we meant the exact same car with the same plate number (and serial number). Identical here would be understood only to mean we were driving the same make, model, year, and color vehicle. Even saying "the exact same" car would still be understood to mean a car exactly like the other car, not the car itself.

Look at NOAD's list of synonyms for identical:

identical adjective 1 wearing identical badges: indistinguishable, (exactly) the same, uniform, twin, duplicate, interchangeable, synonymous, undifferentiated, equivalent, homogeneous, of a piece, cut from the same cloth; alike, like, matching, like (two) peas in a pod; similar.

Not one of those synonyms expresses anything like the Law of Identity (A = A) in mathematics or the strict equality operator in some programming languages (=== instead of ==), even though the root of the word identical is, in fact, the same as for identity: Latin idem meaning "the same".

Even when we speak of things that point to identity, such as fingerprints or DNA, saying that a sample of DNA is identical to the DNA found at a crime scene does not mean the strands are the same strands, but that they come from the same person.

Solution 2:

I don't think English has any "frequently-used ordinary words" to make this distinction.

How often does it come up in ordinary speech that this distinction is important? My guess is rarely if ever. In certain types of technical discussion this distinction is important, and that's why there are technical terms to distinguish equivalence and equality.

However, distinctions that are not relevant in ordinary conversations don't generally have frequently-used ordinary words to distinguish them. On the occasions that this distinction does come up and is not obvious from context (such as the situations invented in some of the answers and comments here), the distinction is made either using technical terms or using description.

Solution 3:

I can't think of any words that would be a direct replacement for “same” in your examples, but it's possible to express the distinction.

Alice and Bob share a car.

A single car between them. In Python syntax, Alice.car is Bob.car.

Alice and Bob have identical cars.

Two cars (note the plural form) that have the same year, make, model, and color. Alice.car == Bob.car.

Solution 4:

How about the very same?

I'm wearing the same dress as Mary.

And

I'm wearing the very same dress I wore a year ago.

The very same will be the identical object.