Venn diagram, comprising two overlapping circles. Circle 1 represents time travel fiction whereas Circle 2 represents alternative history fiction:
inside Circle 1 but outside the area of overlap are (among many other works) Poul Anderson's The Corridors Of Time and There Will Be Time, each describing time travel in a single consistent timeline with circular causality but no causality violation, therefore neither access to nor generation of any alternative histories;
inside Circle 2 but outside the area of overlap are (among many other works) Anderson's "The House of Sorrows," in which the twentieth century is polytheist because the Jews never returned from Babylon, and his "Eutopia," in which the twentieth century is Greek because Alexander the Great did return from Babylon;
inside the area of overlap is Anderson's Time Patrol series, describing time travel in a mutable timeline where several alternative histories are discussed and three are realized, one by extra-temporal intervention, the others by random fluctuations in space-time-energy - whereas the "House of Sorrows" history merely exists and the "Eutopia" history merely coexists with other alternative histories in parallel timelines.
However, all the alternative histories discussed so far contrast with three others presented by Anderson:
in Three Hearts And Three Lions, a man travels from our twentieth century to an Earth on which the Carolingian myths are literally true;
A Midsummer Tempest is set in the seventeenth century of a history where all of Shakespeare's plays, including those featuring supernatural beings and magic, were literally true,
in the two Operation... volumes, twentieth century technology is magical, not scientific.
Clearly, a time criminal in the Time Patrol timeline would be able to generate either the polytheist or the Greek twentieth century merely by diverting the course of history whereas it would be necessary to change the laws of physics in order to generate any of the mythical or magical histories. Let us therefore distinguish between realistic and fantastic alternative histories.
Anderson wrote four volumes of fantastic alternative histories but only two short stories (I think) about realistic alternative histories. By contrast, Anderson's successor, SM Stirling, specializes exclusively in novels and series about realistic alternative histories. I have already discussed three of Stirling's histories and will shortly begin to read Volume I of his Draka tetralogy.