Different terms for 'family' and 'family member'
'家人' is a specific term for 'one's family'


For example: '我的家人在香港' (my family is in Hong Kong)

家人 can also refer to: 'individual(s) of one's family'. For example: '他是陳先生的家人' (He is Mr.Chan's family) 


  '家庭成员' is a specific term for 'member(s) of a family'/ family member(s)


We do not say: " My family members are in Hong Kong." in English; therefore, we don't say: "我的家庭成员在香港." in Chinese neither. 

Similarly, we do not say: "He is Mr. Chan's family member" in English; therefore, we don't say: "他是陳先生的家庭成员" in Chinese neither.


  We use the term '家庭成员' the same as 'family member(s) ' in English. 


For example: 

"Family members of the Chan family includes:  Mr. and Mrs. Chan and their two daughters" (陳家的家庭成員包括：陳先生及夫人及其兩個女兒)

If you say: "Mr. Chan's family, are his wife and two daughters" then the translation would be: "陳先生的家人是他的妻子和兩個女兒”"

If you say: " Mr. Chan's family include he himself, his wife and two daughters" then the translation would be: “陳先生的家庭包括他自己，他的妻子和兩個女兒”


  家庭 is a specific term for "Family"