What is the difference between Consubstantiation and Impanation? I think I'm familiar with Consubstantiation. It is the belief that 


  the fundamental "substance" of the body and blood of Christ are present alongside the substance of the bread and wine, which remain present.


Impanation is a new one for me. I learned it earlier today when reading about John Huss, where it was ascribed to John Wycliffe (oddly, Wikipedia on Wycliffe has no mention of Impanation. Apparently, according to Wikipedia, Impanation is the belief of the 


  the real presence of the body of Jesus Christ in the consecrated bread of the Eucharist that does not imply a change in the substance of either the bread or the body ... This view is similar but not identical to the theory of consubstantiation.


It seems that both descriptions say the same thing. The substance of Christ is present in the bread, but the substance of neither is changed. The only hint I have that they are different is the Impanation definition used "real presence" which is a distinctly Catholic term, and then further insists they are different without explanation.

How are they different? And since I'm unfamiliar with Impanation, what Christian groups are said to believe it?
Impanation is the opposite of Transubstantiation.

Transubstantiation: No Bread. Only Christ.

Consubstantiation: Christ is present along with the bread

Impanation: Christ is present as the substance of bread. That is "Christ has become bread".

The following table might help you understand:

Substance of        |   Bread   |   Christ      | End Result
--------------------------------------------------------------
Transubstantiation  |   ✘       |   ✔           | Bread becomes Christ
Consubstantiation   |   ✔       |   ✔           | Christ is "in, with and under the bread" 
Impanation          |   ✔       |   ☑ as bread  | Christ becomes bread 


The proponents of Impanation believe that it occurs in the same way God (a different type of being) became man. That is, God took humanity and raised it to the level of his divinity. There by sharing his divine attributes with his humanity (like getting into a locked room with his physical body). In the same way Christ's divine attributes are shared by the Eucharistic bread via his body.

Sources:


"Impanation". Catholic Encyclopedia
... impanation, so that the Divinity of the Word is united to the set forth bread of the Eucharist hypostatically.... From The Doctrine of Transubstantiation in the Orthodox Church