At the start of the Neolithic, besides barley, 2 species of wheat were domesticated separately and they evolved through domestication into einkorn wheat and emmer wheat.
Einkorn wheat has always remained a minor crop, while either barley or emmer was the major crop, depending on soil and climate. For instance in the early Ancient Greece barley was the most important, while in the early Roman Republic emmer was the more important. Later, emmer ("far" in Latin) was mostly replaced by durum wheat ("triticum" in Latin), and even later durum wheat was mostly replaced by the hexaploid bread wheat ("siligo" in Latin).
Besides the original emmer and einkorn, other wheat subspecies have appeared many thousands of years later after domestication, either through mutations, like the tetraploid durum wheat (pasta wheat) or through hybridization, like the hexaploid bread wheat (and also the hexaploid spelt wheat).