The sign for "family" is based on a general circle movement
that applies to similar signs such as: family, class, group, and team.
You show the difference between these signs by using initialization (use the
first letter of the represented word as the handshape for the sign).
To sign "family" form "F" hands and use the hands to trace
the shape of a circle. As if representing a family sitting around a dinner
FAMILY DEAF? = "Is anyone in your family Deaf?"
CLASS: As in, I can't wait to go to Dr. Bill's ASL class!"
(Can also be used for "category.")
Note: If you do the sign CLASS with "looser" fingers, it can mean a
"general group of things." I call this the "CLUSTER"
sign. It is often used to show plurality or to
show a "group of things."