Upvote:12
Technically I haven't ever worked for a hotel, but I have worked for over 20 years for half a dozen hostels and one motel.
In natively English speaking countries at least in the accommodation industry, "booking" and "reservation" are 100% synonymous. I wouldn't even say there are any differing nuances or even that one is more formal than the other.
You ask the place to "reserve" a table/room/etc for you and we do that by putting it in a "book". These days the book is usually a computer.
Actually I do have one caveat. Non-native English speakers have begun to refer to the app/website Booking.com as just "Booking", which often confused me as I would think they were talking about their reservation rather than which app they used to make it.