APIs are not the same thing that is mentioned in the analogy of the car and other parts (steering wheel, gear rod, breaks) are interfaces to control the vehicle.

APIs, a framework for writing server-side programming which engineers have built - to make everyone drive the same car.

From the car-side (server) - Make the engine robust to have many potential drivers of the car.

From the driver-side (client) - can I drive the other car, by sitting in my own car, by connecting my steering wheel, gear rod, brakes, clutch of my car, to the API-enabled car?

In this way - a single car (assume that it can be multiplied into many), can be driven by every customer, with their existing controling mechanism, in their own car.

Assumption 1: A company makes a product (API-enabled) and let its 'n' customers access it, without a lag in performance of the application/product/car.

Assumption 2: The car in the analogy is assumed to be multiplyable into many cars, for each customer to drive and control it with their own tools.