I would be grateful if there are any supporters about my question at History.
History recommended and put on hold because the question should be rather asked either at ELU o ELL.
I appreciate any answer in advance.
They both refer to family relationships, though depending on cultural and historical context clan may refer to something broader.
When taking clan to mean strictly a group of people related by blood or marriage, the same meaning as family, it would tend to connote a much more extended relationship group than family. Family can mean something as broad, but usually only does so if context indicates it or you use extra words.
There are, I understand, historical/cultural contexts where it actually meant a family plus other families who were loyal to them.