I understand, however my whole point is that these different other qualities change the shape of the problem (and necessary solutions or impossibilities) completely, often in ways that make it unrealistic for the real-world problems that the paper appeals to in its abstract as motivation. The word "byzantine" is so over-used as well as abused in this field of research, that for a random paper that mentions that word I can't really tell what actual problem it's solving unless I read through it fully in detail. I suggest that a wider more systematic set of terms would help to avoid this problem. e.g. instead of saying "secure" say "unforgeable against a chosen-message adversary" etc.

Lamport's original paper does seem to treat adversaries appropriately, but I've seen many worse papers from recently failing to consider what happens if a malicious peer specifically tries to exploit your "defence" mechanism.