"Shotgun" means two cables, connected in the same way as one another - i.e., both + to + on the amp, and both + to + on the speaker.
"Biwire" means two cables (possibly in a single overall wrapping or sheath), connected together at the amp (i.e., both + to +) but separate at the speaker (i.e., one + to tweeter/high +, the other + to woofer/low +).
"Shotgun biwire" would mean more than two cables (again, possibly in a single wrapping or sheath), but used in a biwire mode (i.e., all + connections connected to + on the amp, two + connections to woofer/low +, a third + connection to + on the tweeter/high +).
More simply, "biwire" to having separate cable paths from high and low sections of a speaker to a single channel on the amp, and "shotgun" to two separate paths that are connected together at both amp and speaker ends.
Oh, and to the best of my knowledge, this terminology is independent of whether the geometry is twisted pair or not - it is about the independent electrical paths and how they are connected at each end.