Why does TypeScript use "Like" types?

Why does TypeScript have a type and then a "like type"? An example of this is Promise<T> and PromiseLike<T>.

What are the differences between these two types? When should I use them? In this case why not just have one Promise type?

If you look at the definition files (let's take lib.es6.d.ts) then it's pretty straight forward.

For example the ArrayLike interface:

interface ArrayLike<T> {
    readonly length: number;
    readonly [n: number]: T;
}

is more limited than the Array one:

interface Array<T> {
    length: number;
    toString(): string;
    toLocaleString(): string;
    push(...items: T[]): number;
    pop(): T | undefined;
    concat(...items: T[][]): T[];
    concat(...items: (T | T[])[]): T[];
    join(separator?: string): string;
    reverse(): T[];
    shift(): T | undefined;
    slice(start?: number, end?: number): T[];
    sort(compareFn?: (a: T, b: T) => number): this;
    splice(start: number, deleteCount?: number): T[];
    splice(start: number, deleteCount: number, ...items: T[]): T[];
    unshift(...items: T[]): number;
    indexOf(searchElement: T, fromIndex?: number): number;
    lastIndexOf(searchElement: T, fromIndex?: number): number;
    
    // lots of other methods such as every, forEach, map, etc

    [n: number]: T;
}

It's good to have the two separated because I might want to have a function like this:

function getSize(arr: Array<any>): number {
    return arr.length;
}

console.log(getSize([1, 2, 3])); // works

But it won't work with this:

function fn() {
    console.log(getSize(arguments)); // error
}

It results with this error:

> Argument of type 'IArguments' is not assignable to parameter of type > 'any[]'.
> Property 'push' is missing in type 'IArguments'.

But both will work if I do this:

function getSize(arr: ArrayLike<any>): number {
    return arr.length;
}

(more on ArrayLike in MDN)

The same with Promise and PromiseLike, if I'm building a library which isn't opinionated about the implementation of the Promise then instead of doing this:

function doSomething(promise: Promise<any>) { ... }

I'll do this:

function doSomething(promise: PromiseLike<any>) { ... }

Then even if the user of my library is using a different implementation (bluebird) it will work just fine.

If you'll notice the definition of Promise is this:

declare var Promise: PromiseConstructor;

Which makes it very specific, other implementations might have different properties, for example a different prototype:

interface PromiseConstructor {
    readonly prototype: Promise<any>;

    ...
}

I guess that the main reason that we have PromiseLike is that several implementations were available before the native one was supported (such as bluebird, Promises/A+, jQuery, and more).
In order for typescript to work with code bases that are using those implementations there must be a type other than Promise, otherwise there would be a lot of contradictions.