In the design of booklets you will have come across two types of spreads. There is a Reader Spread that is used when a booklet is read electronically, so when you open it on your screen, page two is opposite from page three ie. it's what the reader sees. But if you physically take, say a 16pp brochure apart, page two is actually connected to page 15. It is through the binding that the pages will come out in order sequentially. This is a Printer Spread which is what the printer will use in production. Sending through a Reader Spread through to your printer is useless other than providing confirmation of what the finished product must look like.
In fact most printers would prefer not to receive spreads and specifically ask for individual pages supplied in a single pdf. The printers will impose the artwork using their software and how they want to set it up for print given the size of press, the print process and what is being printed. Imposition refers to the placement and direction of pages set up on a press sheet - some pages may appear upside down or backwards, but once the sheet is folded and cut, the pages will be in their proper position and sequence. The resultant double sided group of press sheets for a print job is referred to as a Signature