Copular Clauses -- Predicational, Specificational & Equative

[Morphosyntax]

What is the difference between a specificational copular clause and an equative copular clause?

I know that a predicational CC ascribes a property to the subject, e.g. "Mary is pretty", but I can't quite seem to put my finger on how the two other CCs differ. Both look and feel the same to me, and both can invert.

Spec CC: Mary is the president of the IT club -- The president of the football club is Mary
Equative: Mary is Jane -- Jane is Mary

Is it that in equative CCs, two existing entities are given the same identity, and in specificational CCs,  there's only one entity and that entity is assigned a value?

[Daniel]

I'm not exactly sure on those specific terms, but I think you're referring generally to two well known functions of copulas. One links two things that are equivalent, and another links something to a property.

In the case of two things that are equivalent, you should be able to reverse the order (setting aside pragmatic preferences):
"The doctor is a kind person." > "A kind person is the doctor."
(Admittedly reversing these things has a different tone, and in some cases, such as with pronouns, it sounds very strange, but you get the idea.)

For the descriptive type, it only works in a very poetic sense:
"The book is red." > ?Red is the book.

Is it that in equative CCs, two existing entities are given the same identity, and in specificational CCs,  there's only one entity and that entity is assigned a value?

Yes, that sounds about right. It might oversimplify things regarding whether they are necessarily "entities" or not, but that seems to be the main idea of it.

Note that in Spanish there are actually two different copulas, ser and estar. And at least to some degree they follow this distinction (but not exactly!). Ser is often said to describe "permanent" things, including the equivalence of two nouns. But estar is then said to describe "temporary" things, especially for most adjectives that only apply at the moment. You can actually use either with adjectives, but if you say "soy felíz" (ser.1SG+happy) that means "I'm a happy person", while "estoy felíz" (estar.1SG+happy) means "I'm happy [now]." So that's much more common/natural with estar, because it's describing rather than identifying. Arguably the first type is more like the "equative" type you describe, even though it's not an entity, because it's actually describing the identity of the person as opposed to describing the current state. African American English also does something similar (in a way) where omission of 'be' is used for a current description, while including it is more of an identification: "He sick" = 'he's not feeling well today', vs. "He be sick" = 'he's a sickly person, terminally ill, etc.'.

So maybe the more natural distinction would be between "identifying" and "describing" uses of copulas. Compare also restrictive and nonrestrictive relative clauses:
"You must give $5 to all of the people who are polite."
"You must give $5 to all of the people, who are polite."
Very subtle difference, but the second sentence would mean that "all of the people" are polite. The first just means that you find all of the people who are also polite-- not necessarily all of them. The nonrestrictive type works to identifying who you mean (the second example), while the first actually further restricts the set of people you are referring to. The nonrestrictive type is "optional" in the sense that you have already effectively identified the group (although that additional information can help of course). The restrictive type is not optional because it adds additional (restricting) information.

[Audiendus]

In the case of two things that are equivalent, you should be able to reverse the order (setting aside pragmatic preferences):
"The doctor is a kind person." > "A kind person is the doctor."

I see "a kind person" as a property rather than an equivalent. The doctor is a kind person, but a kind person is not necessarily the doctor. In the reversed form ("A kind person is the doctor"), I would regard "doctor" as the subject and "a kind person" as the subject complement. It could be written with a comma to represent a slight pause ("A kind person, is the doctor." "A strange fellow, is our Jack.")

I think a better example of a copula linking two equivalent things would be: "The doctor is the man on the right". Unlike the example above, this can be reversed without sounding unusual, i.e. "The man on the right is the doctor".

[Daniel]

I see "a kind person" as a property rather than an equivalent.

Kind describes person. But "kind person" = "doctor".

The doctor is a kind person, but a kind person is not necessarily the doctor.

But that particular kind person is. Feel free to switch in a definite form if it's clearer:
"The kind person is the doctor." = "The doctor is the kind person."

In the reversed form ("A kind person is the doctor"), I would regard "doctor" as the subject and "a kind person" as the subject complement. It could be written with a comma to represent a slight pause ("A kind person, is the doctor." "A strange fellow, is our Jack.")

That's not the only interpretation, but it's possible. But I'm not sure why that stylistic variation would have an effect either way in terms of copula type. ("Yellow, is the bus.")

I think a better example of a copula linking two equivalent things would be: "The doctor is the man on the right". Unlike the example above, this can be reversed without sounding unusual, i.e. "The man on the right is the doctor".

Yes. Using any definite form works better (but isn't required and can still work under the right reading otherwise).