Between our book and the film, I think can be seen many parallels, but also differences.
First of all has to be said that both of them play at the beginning of the 1920s in India. Like Olivia, also Mrs. Quested and Mrs. Moore travel to India to get to know better the country, without knowing nothing at all about it. In fact, both arrivals are bound to several difficulties.
In the film, the British live in a kind of ghetto, separated from the Indians and not wanting them in their clubs. In comparison to that, the British in the book live also somehow separate, but in the same town as the Indians. The English mostly maintain their way of life or, for example, take with them their English furnishing. Many of them e.g. Mrs. Saunders treat the “normal” Indians bad and take them as servants. But in difference to “A Passage to India” there are also some royal Indians, the Nawab and his mother. These ones are esteemed very highly. All the English women try to get friends with the Begum and to appeal to her play little roles during the meetings. Such relationships don’t exist in the film. The only one who sees the Indian from an other point of view is Richard Fielding.
The further action differentiates only a bit, but the outcome is totally different. Mrs. Quested expresses the wish to get to knew better the landscape, so a trip to the holes nearby the town is planned. At the same time, in the book, both Olivia and the narrator go to visit the shrine. There nothing happens, in the holes, however, Mrs. Quested gets panicked and has an accident saying later that Dr. Aziz has followed her.
In Heat and Dust no one really gets in trouble like that, the gap between Indians and British isn’t that big.
The only parallel between those visits is maybe, that Dr. Aziz and also the Nawab or Inder Lal arrange the visit very extensively to awake the interest of Mrs. Quested, Olivia, or the narrator.
In the end, Adela returns to England, Richard marries the daughter of Mrs. Moore and also Dr. Aziz has two children. That stands in an absolute contradiction with Heat and Dust. There Olivia escapes with the Nawab and lives in a house in the mountains in India, where the climate is much more comfortable that in town. Also the narrator, who is getting a child from an Indian goes there, to bear her child.