Bi-wire cables(speaker) are cables that have a pair of connectors(be it spade, bananas, pins, bare wire etc.) at the amp end and two pairs of connectors at the speaker end in a single cable run (L or R channel for example). The latter is for connecting it to a two way (2 separate binding post; normally configured as mid and hi on top and woofer at the bottom)speaker.
Bi-wire shotguns(can also be identified as external bi-wire) are cables with two separate runs for each channel joined at the amp ends. You still have four connectors at the speaker end but instead of being encase in a single cable housing or insulation, you have two. The amp ends which are joined together and the same as a bi-wire config.
Internal bi-wire, on the other hand, is also the same as bi-wire except two complete runs of wires are encased in a single cable body per channel.
There are no concrete evidence as far as the superiority of one config to the other. In fact some people claim that single run with better jumpers works well than bi-wire. Also, there are papers that contest the advantage of bi-wiring and explains its disadvantages especially on speakers with passive cross overs. Do your research before you decide. In the end, what sounds great to you matters. Also, bi-wire cables are expensive compared to their single run counterparts. Some speaker manufacturers recommends bi-wiring. Conversely, some cautions their customers that there is no difference in performance.
....to inform, and not to convince...