Books are not sold to publishers; technically they are licensed. The publisher buys certain rights from the author in exchange for varying percentages of the cover price per copy sold. In the U.S. the normal rights that are licensed for books are what are called, inaccurately, First North American rights. That means that the publisher has the right to first sell and distribute the book in the U.S. and in Canada. (Not in Mexico or Central America, though.)
Foreign rights allow the book to be published in other countries. Normally a publisher in a country will bid for the right to publish the book on its own presses. A U.K. publisher will license the rights to a book (which may include the right to distribute and sell it in other Commonwealth countries) and that allows it to do pretty much anything it wants with the outside of a book, to better ensure the best possible theoretical sales. So the title, the covers, the blurbs, the author’s photo - any and all of these might be changed if they think it will make the book sell better.
It works the same way in reverse as well, with U.K. publishers licensing U.S. publishers rights.
The actual text of a book is unlikely to be altered, except if it is thought that the differences in spelling and word meaning will get in the audience’s way. This was notoriously the case with Harry Potter. The U.S. publisher thought the American audience wouldn’t get “Philosopher’s Stone” and so changed it to the more easily graspable “Sorcerer’s Stone.” I understand that other Briticisms were also changed in the text itself. I’m pretty sure that this no longer happens, but that’s only because of the enormous clout that Rowling now has, not because publishers have changed their opinion of the American audience.
Just for completeness, foreign language editions are treated in the same way. Each publisher licenses the rights for a particular language and has its own translator redo the text. The new text is copyrighted in both the name of the author and of the translator.
Again, the cover and title may be completely different. I had one of my books published in several European countries and I liked every single one of the covers far better than the plain text my U.S. publisher used.