Before revision:  The stronger adaptation --- individual fairness--- requires that each individual in each familyperceives the division as fair ; the weaker one --- family fairness --- requires that the familyas a whole, treated as a single agent with (typically ) incomplete preferences, perceives the division as fair. Individual-fair-share, family-no-envy and family-egalitarian-equivalence are compatible with efficiency under broad conditions. The same holds for individual-no-envy when there are only two families. In contrast, individual-no-envy with three or more families  and individual-egalitarian-equivalence with two or more familiesare typically incompatible with efficiency, unlike the situation in an economy of individuals.
After revision:  For any given criterion of fairness, an allocation is *unanimous-fair* if it is fair according to every individual member of each family, it is *aggregate-fair* if it is fair according to a particular aggregation of all family members' preferences, and it is *collective-fair* if it is fair according to the family's -- typically incomplete -- preferences, that rank a bundle above another bundle if and only if each member of the family ranks the first bundle above the second. While efficiency is generally incompatible with unanimous egalitarian equivalence, and incompatible with unanimous envy-freeness in economies with three or more families and individual-egalitarian-equivalence with two or more familiesare typically incompatible with efficiency, unlike the situation in an economy of individuals.