Dark current happens always, light or no light. Photons can be striking the pixels or not, dark current will accumulate regardless...but I think it is misleading to say that it occurs when no photons are present.
Fixed pattern noise usually refers to the hot and cold pixel pattern that is actually revealed by the accumulation of both dark current and photons over longer exposures (or highly amplified exposures at very high ISO.) It's fixed because it arises due to physical traits of the silicon itself, slightly differing response to dark current.
Banding is a form of structured, but not necessarily patterned, noise. It has structure, often semi-random, in that the bands may occur in the same place across frames, but are not guaranteed to occur in the same place across frames (or occur at all for a given set of frames.) Banding can present in a variety of ways as well. For example, a 300-frame master bias from a 7D presents a very pronounced 8-column wide vertical banding structure, which corresponds with the 8 readout channels. Banding can also be much softer, spanning multiple columns, although which columns are affected can be random from frame to frame. So...structured, but not necessarily a *fixed* pattern.
Banding could be caused by external interference...possibly because the electronics of the camera itself are not properly shielded.
There are other forms of noise. Salt and pepper noise, for example (a problem that occurred on the 5D II), appears like hot and cold pixels, but it is effectively a random distribution of white and black pixels. The distribution may not be the same frame to frame, and it is not a thermal signal, so sigma clipping is the only real means of eliminating it.