This is fairly common, many people describe exams to be among the more stressful events in their lives.
Interviews are always exams, whether it's writing code on a whiteboard or trying to figure out what the interviewer wants to hear about where you see yourself in 5 years.
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.
Interviews are always exams, whether it's writing code on a whiteboard or trying to figure out what the interviewer wants to hear about where you see yourself in 5 years.