Vent free fireboxes are generic fireboxes that can be installed virtually anywhere in the house as they do not require venting and can be installed in the combustible framing.
They can be louvered (a.k.a. circulating), which means that they are capable of having a fan, but they look industrial, because the louvers have to be exposed and cannot be covered with anything. The other type of the vent free firebox is radiant (i.e. clean face) and it can be finished with non-combustible material of choice right up to the edge of the opening. This type of fireboxes cannot have a blower, though.
Any of the generic fireboxes can accept a properly sized vent free burner / log set.
The only difference between vent free fireboxes and vent free fireplaces is that the latter has a vent free burner integrated with its body.