Genealogy
For reference, the Board for Certification of Genealogists (based in the US) defines Genealogy with:
Genealogy is the study of families in genetic and historical context. Within that framework, it is the study of the people who compose a family and the relationships among them. At the individual level, it is biography, because we must reconstruct each individual life in order to separate each person’s identity from that of others bearing the same name. Beyond this, many researchers also find that genealogy is a study of communities because kinship networks have long been the threads that create the fabric of each community’s social life, politics, and economy.
The Society of Genealogists (SoG) (based in the UK) defines Genealogy with:
Establishment of a Pedigree by extracting evidence, from valid sources, of how one generation is connected to the next. (In essence, this means the discipline of the construction of a valid family tree)
Family History
The SoG defines Family History as:
A biographical study of a genealogically proven family and of the community and country in which they lived. (In essence, this means the writing of a biography of a series of related ancestors of common genealogy. Family History incorporates Genealogy)
Microhistory
Here at the Genealogy and Family History Stack Exchange we recognize that the study of related Microhistory such as the history of a building, ship, village, etc can be very useful when trying to understand the history of a family who lived in or travelled on them.