Is it spread “syntax” or the spread “operator”?

It’s not an operator.

In all senses of the word, it’s not one. It has been a huge misconception since it was introduced and despite popular opinion — it’s not one, and there are a few objective points to be made:

• It doesn’t fit the definition of an operator
• It can’t be used as an operator
• The language specification implies that it’s not an operator

It should be mentioned that spread syntax comes in different ‘flavors’, used in different contexts and are commonly referred to by different names while using the same punctuator. Spread syntax is basically an umbrella term for the application of the ... punctuator, and see Felix Kling‘s great answer detailing all the uses and names. More explanation about these individuals uses is given in the supplementary answer.

What is an operator?

Semantically, in the context of ECMAScript, operators are just builtin functions that take in arguments and evaluate to a single value — written in prefix, infix, or postfix notation and usually with symbolic names such as + or /. From Wikipedia:

Simply, an expression involving an operator is evaluated in some way, and the resulting value may be just a value (an r-value), or may be an object allowing assignment (an l-value).

For example, the + operator results in a value such as 2, which is a right-hand-side expression, and the . operator results in an object allowing assignment such as foo.bar, a left-hand-side expression.

On the surface, the ... punctuator¹ looks to be a prefix unary operator:

const baz = [foo, ...bar];

But the problem with that argument is that ...bar doesn’t evaluate to a singular value; it spreads the iterable bar‘s elements, one by one. The same goes for spread arguments:

foo(...bar);

Here, foo receives separate arguments from the iterable bar. They’re separate values being passed to foo, not just one value. It doesn’t fit the definition of an operator, so it isn’t one.

Why isn’t it an operator?

Another point to be made is that operators are meant to be standalone and return a single value. For example:

const bar = [...foo];

As already mentioned, this works well. The problem arises when you try to do this:

const bar = ...foo;

If spread syntax were an operator, the latter would work fine because operators evaluate the expression to a single value but spread doesn’t so it fails. Spread syntax and spread arguments only work in the context of arrays and function calls because those structures receive multiple values supplied by spreading array elements or arguments. Evaluating to multiple values is outside of the scope of what an operator is able to do.

What do the standards say?

The complete list of operators is listed in Clauses §12.5 through §12.15 in the ECMAScript 2015 Language Specification, the specification in which ... is introduced, which doesn’t mention .... It can also be inferred that it’s not an operator. The two main cases mentioned in this answer in which spread syntax is in a production, for function calls (spread arguments) or array literals (spread syntax) are described below:

ArrayLiteral :
  [ Elisionopt ]
  [ ElementList ]
  [ ElementList , Elisionopt ]

ElementList :
  Elisionopt AssignmentExpression
  Elisionopt SpreadElement
  ElementList , Elisionopt AssignmentExpression
  ElementList , Elisionopt SpreadElement

Elision :
  ,
  Elision ,

SpreadElement :
  ... AssignmentExpression
  

And for function calls:

CallExpression :
  MemberExpression Arguments

Arguments :
  ( )
  ( ArgumentList )

ArgumentList :
  AssignmentExpression
  ... AssignmentExpression
  ArgumentList , AssignmentExpression
  ArgumentList , ... AssignmentExpression
  

In these productions, there’s a conclusion that can be made: that the spread ‘operator’ doesn’t exist. As mentioned earlier, operators should be standalone, as in const bar = ...foo and evaluate to one single value. The syntax of the language prevents this, which means spread syntax was never meant to be standalone. It’s an extension to array initializers and function calls, an extension to their grammar.

Why spread ‘syntax’?

Syntax, as defined by Wikipedia:

In computer science, the syntax of a computer language is the set of rules that defines the combinations of symbols that are considered to be a correctly structured document or fragment in that language.

Syntax is basically the ‘form’ of the language, rules that govern what is legal or not regarding how the code should look, and how the code should be written. In this case, ECMAScript’s grammar specifically defines the ... punctuator to only appear in function calls and array literals as an extension — which is a rule that defines a combination of symbols (...foo) that are considered to be legal together, thus it is syntax similar to how an arrow function (=>) is not an operator, but syntax².

Calling ... an operator is a misnomer. An operator is a builtin function that takes in arguments (operands) and is in the form of prefix, infix, or postfix notation and evaluates to exactly one value. ..., while satisfying the first two conditions, does not satisfy the last. ..., instead, is syntax because it is defined specifically and explicitly in the language’s grammar. Thus, ‘the spread operator’ is objectively more correctly referred to as ‘spread syntax’.

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¹ The term ‘punctuator’ refers to punctuators in ECMAScript 2015 and later specifications. These symbols include syntax components and operators, and are punctators of the language. ... is a punctuator itself, but the term ‘spread syntax’ refers to the whole application of the punctuator.

² => itself is a punctuator, just as ... but what I’m referring to specifically is arrow function syntax, the application of the => punctuator ((…) => { … }), just as spread syntax refers to the application of the ... punctuator.