previous post differentiated:
(i) fantastic alternative histories;
(ii) realistic alternative histories;
(iii) realistic alternative histories generated by time travel;
(iv) time travel unable to generate alternative histories.
Poul Anderson wrote (i) - (iv) although less (ii). However, his Time Patrol series, which includes works of category (iii), clearly shows that he could have written more (ii). Either kind of alternative history can be presented as just a single timeline or as one of many, with the possibility of travel between them. Again, Anderson did both.
SM Stirling is a master of (ii). I have just begun to read Stirling's Marching Through Georgia, which starts its action in what is clearly an alternative history without as yet referring to any multiplicity of such histories. However, the series is four volumes in length so anything can happen and probably does.