[logfromblammo]

Two duress codes--one for you, and one for your counterparty. Thus, the bi- in bi-deniable.

Mono-deniable gives a duress code only to the sender, or only to the recipient.

The paper claims an additional category of bi-deniability, such that your duress code and your counterparty's duress code produce different plaintexts, rather than the same plaintext. It is unclear from the abstract whether it is possible to have a bi-deniable scheme without this property (which does not also require prior coordination between parties).