Alternative Histories In Fantasy And SF

An sf alternative history assumes the same physical laws as in our universe. Only the course of history has diverged, e.g., in Poul Anderson's "Eutopia" or his "The House of Sorrows."  However, these are two short stories. Anderson's four alternative history novels are set in universes where magic works and thus are fantasies, not sf. In the two further short stories that are set inside the inter-cosmic inn, the Old Phoenix, the inn is accessed by travelers from both kinds of universe, thus magic works in some of the universes although not in others.

SM Stirling's alternative history novels present entirely science fictional scenarios:

Nantucket 1998 A.D. changes places with Nantucket 1250 B.C.;

"On October 3, 1878, the first of a series of high-velocity heavenly bodies struck the earth." (The Peshawar Lancers, p. 459);

on April 17, 1946, the far wall of John Rolfe's basement was replaced by a rippling silver sheet...;

on July 1st, 2014, "The richest man in the world liked eating pastrami sandwiches in orbit..." (The Domination, p. 1);

on May 21, 442nd Year of the Final Society (2442 A.D.), "Gwendolyn Ingolfsson stood naked beside the stream.'" (Drakon, p. 1);

on Labor Day, 1962, sf writers at the World Science Fiction Convention in Chicago watched TV coverage of First Contact with Martians...

These are different timelines with three common features:

all emerge from the imagination of a single writer;
all are hard sf;
they could be incorporated into a single fictional multiverse.