Alternative (or in the USA, alternate) history is a genre of fiction where the world has taken a different turn some time in the past, and has produced a timeline which differs from ours. In that the events described in the book rely on a distortion of history prior to those events, it may be seen as different from historical science fiction.
In this latter category, I think we have to place Susanna Clarke’s magnificent magical (in every sense of the word) tour de force, Jonathan Strange and Mr. Norrell, although it deals with people and places and events (the Duke of Wellington, Waterloo) in our world, together with others (John Uskglass, Faerie, etc.), that though meticulously described, have no counterpart in real life.
There are several popular points of departure for alternative fiction. One of the most common, especially in the USA, is the idea that the Confederacy won the Civil War. The idea has been explored in several works, notably Kevin Wilmott’s fine “mockumentary” C.S.A.: The Confederate States of America.
Another popular point of departure is one where the Axis, usually reduced to simply the NSDAP (Nazis), but sometimes including the Japanese, have won the Second World War. Len Deighton’s SS-GB is one of the best of these, and Philip K. Dick’s The Man in the High Castle takes things one or two steps further, postulating a world in which the Axis won, but where there is an underground samizdat novel circulating in which the Allies won the war.
There are other, more esoteric, points of departure, such as the idea that the Spanish Armarda was successful in its attempt to re-impose Catholicism on the English, or that the Gunpowder Plot succeeded, and James I and VI and his family were wiped out, leading to a Tudor restoration, or that Nelson was killed earlier in the Battle of Trafalgar, leading to the eventual incorporation of the British Isles in Napoléon Bonaparte’s Empire.
In any event, I find “what if”s or counterfactuals to be fascinating, and I’ve produced two books in the genre. I have also started another one, a sample of which may be found on the page about these books.