|A hardback, a trade paperback and a mass market paperback|
I can't claim absolute knowledge, but this is my understanding of what's going on. Broadly there are three formats a typical fiction or non-fiction book (i.e. not a picture book, textbook etc.) can be published in: hardback, trade paperback and mass market paperback. In very broad terms the price points for these in the UK are typically £18.99, £12.99 and £8.99 respectively. A book will typically be brought out in either one or two of these categories (not usually simultaneously).
The price differential is not really about manufacturing costs. The differences per book for the same size print run is in pennies, not pounds. The more expensive end is a premium product, rather like a designer label or organic food - it's no better technically, but some people are prepared to pay more for it.
Many relatively unknown authors are puzzled as to why publishers will first issue their books as a hardback or a trade paperback. Surely, the public is more likely to take a punt on an unknown author if the book is as cheap as possible? I've argued this way myself in the past.
There seem to be two reasons for producing the premium books. One is that for a book that is going to sell anyway, it's worth reaping that premium from those who are prepared to pay it, either to get the book earlier, or because it makes a better gift. The second is that for some reason many of the traditional reviewers (like newspapers) treat mass market paperbacks as secondhand citizens. I don't understand this, but it's the way things are. If you want plenty of reviews, going straight to a basic paperback is not going to help.
The trade paperback is a kind of intermediate format. It is a posh paperback - usually larger than the mass market version and with a smarter cover. It may well have texture on the cover and fold-out flaps, and it will be a bit larger than its mass market equivalent. It seems to be sufficient to get the attention of the reviewers, and gives some premium income, so is increasingly used as an alternative to a hardback.
After that initial push, from the publisher's viewpoint being a hardback or trade paperback can be a bit of a liability, so if the book is doing well, a mass market paperback is liable to follow. This is partly to enable economies of scale, but also reflects the fact that most bookshops only stock a relatively small number of hardbacks. Although it can be easier to get a hardback into a review, it is certainly easier to get a paperback into a shop.
The extreme version of this is well illustrated by my book The First Scientist. A scientific biography of the 13th century friar/proto-scientist Roger Bacon this was a book that was unlikely to get out of hardback. Yet when that proved a rather slow mover, the US publisher took a batch of hardbacks, cut off the hardcover and replaced it with a paper cover so they would have a better chance of getting into bookshops.