The terms "archaeology" and "archeology" refer to the same field of study, which involves the examination of human history and prehistory through the excavation and analysis of artifacts, structures, and other physical remains.
The difference lies primarily in spelling, which is influenced by regional language preferences:
Despite the spelling differences, both terms describe the same academic discipline and practical field, encompassing the study of ancient and historical human activity through material remains.
In essence, there is no difference in meaning; only the spelling varies depending on regional language conventions.