According to MDN:

An expression is any valid unit of code that resolves to a value.

As such, anything that can be used as an rvalue is an expression.

The criterion is not whether side effects exist. Expressions can definitely have side effects. E.g. a=2 is an expression as it has a value (2) and also assigns a value to a variable. Which is why you can do things like:

let a;
let b = 1 + (a = 2); // a is now 2 and b is 3

It is possible for the same (textual) block of code to be considered both an expression and a statement depending on the context. E.g. the text snippet function f(){} is an expression on line 1 and a statement in line 2 in the below code:

let g = function f() {};
function f() {};

So whether something is an expression or a statement cannot (in the general case) be determined by looking at a textual piece of code out of context; rather it is a property of a node in a syntax tree and can be decided only after the code is (mentally or actually) parsed.

Also, and perhaps more importantly, function statements (a.k.a function declarations) inside a function f form part of the execution context that gets created when function f is invoked. However, function expressions do not form part of that execution context.

One often quoted effect of that is that function declarations get "hoisted" whereas function expressions do not.

A more subtle effect can also be experimentally observed in deep recursions given that function statements take up space in the execution context whereas function expressions do not. E.g. the below code uses infinite recursion of a function f. Function f in the first case includes a function expression inside it, in the second case it includes the equivalent function declaration:

// Function Expression
{
    let i = 0;
    try {

        function f () {
            i++;
            (function g() {})(); // this is an expression
            f();
        }

        f();

    } catch (err) {
        console.log(`Function Expressions case: depth of ${i} reached. Error: ${err.name}`);
    }
}
// Function Declaration
{
    let i = 0;
    try {
        function f () {
            i++;
            function g() {}; // this is a statement
            g();
            f();
        }

        f();

    } catch (err) {
        console.log(`Functions Declarations case: depth of ${i} reached. Error: ${err.name}`);
    }
}

On my machine I consistently get the following (in node.js):

Function Expressions case: depth of 17687 reached. Error: RangeError
Functions Declarations case: depth of 15476 reached. Error: RangeError

… which is consistent with the fact that Function Declarations increase the amount of space necessary to hold an execution context and thus eat up stack space a little faster and so slightly decrease the maximum recursion depth.