Difference lies in access control.
In a Family Account, you retain full control of the account, even if the account is for someone else.
The person whose Family Account you've been operating is completely dependent on you, to give them order updates and holding related updates.
Managed Account is the opposite of that. Here, the owner of the account retains control of the account, and gives read access to the Manager. Execute or write access has to be validated by the owner of the account.
There are times when you'd want to create a Family Account for a member. And there are times, when you simply want to add a manager to your account.