How do caraway and ajwain differ in taste and use?
Ajwain is a plant in the family apiaceae, and its seed, which is used (especially in south Asian cooking) for its thyme-like flavor while caraway is a biennial plant, native to Europe and Asia, mainly grown for its seed to be used as a culinary spice. 

Ajwain is used more for saviory dishes for it's thyme like qualities, while caraway is more used in baked goods similar to how aniseed is used.