Optical coherence versus quantum coherence
Coherence is the ability to track the phase of a wave. In optical coherence, a light source is coherent in time/space if you can determine the phase difference between two points in time/space. For an incoherent light source, one cannot perform Young double slit experiment or just a simple Michelson interferometer, because these require a stable interference pattern, and when the phase difference is too noisy, the interference pattern fluctuates rapidly from constructive to destructive interference and on average it seems like there is no interference.
Quantum coherence is the same principle - in quantum mechanics effects of superposition show how states interfere with one another, and losing track of the phase difference between the states - that's what quantum decoherence is all about, quantum effects average to the case of no interference because of the fluctuating phase.
And finally, the coherent state is just a special state that is useful in quantum optics to describe the state of light coming out of lasers - not with a certain amount of photons but a superposition that looks like a regular EM wave in time.