What do different types of SDI mean?
SDI stands for Serial Digital Interface.  Over time, the bandwidth needs of video have changed drastically, and so SDI has gone through a number of revisions and different solutions for handling the ever increasing bandwidth loads.

3G, 6G and 12G SDI all refer to single conductor bandwidth specs.  They refer to the maximum data rate supported.  3G is capable of 3 gigabit transmission, 6G up to 6 gigabit and 12G up to 12 gigabit.  Each standard uses progressively higher grade cables and more rigorous transmission standards to enable the higher data throughput.

Dual and Quad link SDI take an alternate approach.  They use the slower SDI cables, but run multiple cables to the same device.  Using this approach, it is possible to split the data and achieve higher throughput with lower grade (and potentially pre-existing) cabling, but multiple conductors are required.

The standard you use will be determined by the feeds that both your source and destination devices can support and based on the wiring constraints you decide on (length of run and cable costs being the main two factors, as well as any existing wiring).

Much more technical detail on SDI is available on Wikipedia.