[bonoboTP]

I don't think there's a consistent terminology. In my computer vision class we called it "object recognition" when it was about recognizing one specific object (this particular car) and "object classification" when deciding the category of the object in the image (in general, like 'car', 'bottle').

One may also call the localization of the object as object detection and subsequent classification.

But I don't think it's too important how we call it as long as we understand what the task is.