After three I can say that indeed, every birth is different, and every hospital is, too.
My first-born, who I had when I was only 20, was born in Berlin and people were very nice and considerate, and him being the first, it took some 9 hours of really regular contractions for the pushy part to begin - which took me totally by surprise by its intensity. I was so NOT prepared for the huge urge to push that is suddenly there and cannot be controlled!
I HAD TO control it, all the same, when my second child was born almost 9 years later and nothing, but nothing at all, had prepared me for a labour duration of only barely 2 hours before the urge to push set in - which it did, when we had only JUST arrived at the parking of the hospital and my husband had walked up the ambulance path to announce our arrival. By the time he came back, I was panting "I'm having the baby - NOW" and he ran back to call for help, all six or seven of who came RUNNING (whoa! I did that, heehee!) with a stretcher on wheels, and with a few very clear words (sounded much like SHOUTING to me at the time, which I guess it was, but else I would not have got out of that car ever) made me climb onto that stretcher, telling me to yelp and pant like a dog as to suppress the urge to push, then ran through the hall with me to the elevator, which was OUT OF ORDER :shock:, so back again through the hall to the OTHER elevator, and up to the maternity ward, where there were major renovation works being done, so they crashed me into the ladder of one of the painters there (fortunately there was no painter standing on that ladder at the time), and on went their frantic race to the delivery room with me, struggling against this enormous desire to push, in their middle. Within a minute inside the delivery room, my son was born.
My daughter took a lot longer. Not that very many more hours of contractions passed, but when she was about to come out, she didn't. And the midwife was at a total loss. For 2 1/2 hours I pushed and tried... no luck. By the time I was so far away in my own little world of only wishing this child to come out at last, I never realised they had made the phone call to the operation theatre to get ready for a c-section. Then the morning shift midwife arrived, examined me and said: Hey, this is the third, we'll get it the natural way!
She had found out that my daughter's head was tilted to her shoulder, so she deftly pushed her back up, adjusted her head, and within 30 minutes, she was born. 2 1/2 hours later, we left the hospital as a (bigger) family. All's well that ends well.