This is from Steve Turpin on the same question on FB
Our family has used the terms "Hen box" and "Standard box" as an informal way for us to distinguish between the two styles of handled and non handled boxes. Turpin Hen boxes have handles and Turpin Standard boxes do not. Then people shortened this and just started calling them a Hen box and Turpin box. Turpin Hen boxes have handles and Turpin Standard boxes do not. If I modified a Turpin standard box call by putting a handle on it, it would then become a Turpin hen box. The standard box is generally a little larger body sized call (but it doesnt have to be) with about the same overall length as a hen box including the handle.