Russian words for reservation

I am curious on if Russian words for reservations are interchangeable.

For example - I have reserved a restaurant before by saying "хочу заказать"
What is the difference between this and say "бронированиe" or "резервирование"

And since we're on this topic, for hotel rooms, are the words "номер" and "комната" also interchangeable?

"бронировать" is used more in hotel/transport business (object is place/seat). "резервировать" is used more in shopping business (object is item).
However they mean exactly the same and there is no mistake in interchanging.
"Заказать" is "to order", that is first step in purchase with delayed delivery/receipt. So, it's suitable term for reservation of room in hotel, however meaning is not the same.

"are the words "номер" and "комната" also interchangeable?" - yes.

Alex, this is excellent explanation. Thank you! Brushing up on my Russian for trip to Moscow/ SPB soon.