In a way, yes. But by blurring this distinction, you make it impossible to distinguish between an hour at the whiteboard solving a data structures problem, and an hour answering questions like "tell me about a time you overcame a challenge and what you learned".

Because people outside our field experience interviews in the second way more often, I think they don't fully understand what goes on in google style interviews. This is why I would call what we go through "Exam-style interviews", drawing a distinction between the two - even though I agree with you that they have elements in common.