Difference between extending and intersecting interfaces in TypeScript?

Let's say the following type is defined:

interface Shape {
  color: string;
}

Now, consider the following ways to add additional properties to this type:

Extension

interface Square extends Shape {
  sideLength: number;
}

Intersection

type Square = Shape & {
  sideLength: number;
}

What is the difference between both approaches?

And, for sake of completeness and out of curiosity, are there other ways to yield comparable results?

Yes there are differences which may or may not be relevant in your scenario.

Perhaps the most significant is the difference in how members with the same property key are handled when present in both types.

Consider:

interface NumberToStringConverter {
  convert: (value: number) => string;
}

interface BidirectionalStringNumberConverter extends NumberToStringConverter {
  convert: (value: string) => number;
}

The extends above results in an error because the derriving interface declares a property with the same key as one in the derived interface but with an incompatible signature.

error TS2430: Interface 'BidirectionalStringNumberConverter' incorrectly extends interface 'NumberToStringConverter'.

  Types of property 'convert' are incompatible.
      Type '(value: string) => number' is not assignable to type '(value: number) => string'.
          Types of parameters 'value' and 'value' are incompatible.
              Type 'number' is not assignable to type 'string'.

However, if we employ intersection types

type NumberToStringConverter = {
  convert: (value: number) => string;
}

type BidirectionalStringNumberConverter = NumberToStringConverter & {
  convert: (value: string) => number;
}

There is no error whatsoever and further given

// And this is a good thing indeed as a value conforming to the type is easily conceived
const converter: BidirectionalStringNumberConverter = {
    convert: (value: string | number) => {
        return (typeof value === 'string' ? Number(value) : String(value)) as string & number; // type assertion is an unfortunately necessary hack.
    }
}

const s: string = converter.convert(0); // `convert`'s call signature comes from `NumberToStringConverter`

const n: number = converter.convert('a'); // `convert`'s call signature comes from `BidirectionalStringNumberConverter`

Playground Link

This leads to another interesting difference, interface declarations are open ended. New members can be added anywhere because multiple interface declarations with same name in the same declaration space are merged.

Here is a common use for merging behavior

lib.d.ts

interface Array<T> {
  // map, filter, etc.
}

array-flat-map-polyfill.ts

interface Array<T> {
  flatMap<R>(f: (x: T) => R[]): R[];
}

if (typeof Array.prototype.flatMap !== 'function') {
  Array.prototype.flatMap = function (f) { 
    // Implementation simplified for exposition. 
    return this.map(f).reduce((xs, ys) => [...xs, ...ys], []);
  }
}

Notice how no extends clause is present, although specified in separate files the interfaces are both in the global scope and are merged by name into a single logical interface declaration that has both sets of members. (the same can be done for module scoped declarations with slightly different syntax)

By contrast, intersection types, as stored in a type declaration, are closed, not subject to merging.

There are many, many differences. You can read more about both constructs in the TypeScript Handbook. The Interfaces and Advanced Types section are particularly relevant.