How do the differences between the replicants and Deckard evolve in Blade Runner?

Actually, the movie is quite ambiguous about whether Deckard is actually a human or a replicant, Ridley Scott takes him as a replicant, while Harrison Ford believes he is human. Even though Deckard shows more and more emotions as the movie goes on, the same is true about the other replicants.

The ambiguity is IMHO, indeed an important part of the point of the movie (and the original novel) – what is the difference between humans and machines. And (a persistent theme in P.K.Dick’s works) how can you be sure you are, in fact, a human, not a machine?

See also: Deckard: human or replicant?

The novel is less subtle about posing the question about who is an android or not. In the novel Deckard goes to retire an android who makes a phone call for help before being killed. The police who show up are from a 'shadow' police department who are nearly all androids themselves living under cover. Deckard escapes with a blade-runner who works with this fake police department who didn't realize he was working with androids and perhaps was even 'retiring' humans. Deckard and the second blade runner debate who is an android and who is human, and who should take the 'test'. Adding to confusion, they both have different tests they use. The novel had already introduced Rachel, the android who believed she was Tyrrel's niece, to lay the ground for androids who do not know they are not human. In addition, throughout the book there is a major plot thread about his electric sheep and whether he lacked empathy by not purchasing a real pet.

The movie does not include many of the plot elements from the novel, but it more subtly introduces the question about whether Decker is an android or not. It leaves the viewer with many more open questions and is as a result an excellent but different story.

I think that has to do the book, the movie adapts. In Do Androids Dream of Electric Sheep? all people are a bit like zombies, they only want to go away from earth or follow a strange religion like Deckards wife does. In a scene in the book, another Blade Runner suspects Deckard to be a replicant and makes a test with him. I think, Philip K. Dick wanted to show, that the difference between humans and machines isn't that big, as we think.

In the movie Ridley Scott seems to make a little different point. For me the movie said, that androids are able to the same emotions and empathy as humans, if they develop it (so states the theory, that humanity is developed). Deckard makes like Rachel and Roy the progress to humanity, although they take different directions.