What is the difference between general purpose ADCs, Audio ADCs and video ADCs?
First, I think you use the word "merely" very lightly.  ADCs are some of the most complex, challenging mixed-signal systems in use.  To meet different performance targets practical ADCs use many different architectures (the most important right now are sigma-delta,  SAR, and Pipelined).

ADC design is characterized by very painful tradeoffs between speed, accuracy, noise, and power dissipation.  For example, to increase the SNDR of a thermal-noise limited ADC by one bit increases the power roughly 4X (because noise is proportional to sqrt(C)).

To first order (and this is VERY rough, mind) you can think of the speed-accuracy product of an ADC to be constant.  So, to make an ADC very accurate it must be slow, and, conversely, the fastest ADCs (now at 40 GS/s and beyond) have very low resolutions (4 - 6 bits or so).  This is due to a combination of factors such as oversampling (taking multiple samples and averaging) which reduces the speed, and the capabilities of sample-and-hold circuits to acquire signals at needed accuracy (for example, a 10-bit sample-and-hold needs to sample the input signal to an accuracy of about 0.1%.  A 16-bit sample-and-hold needs to sample the input to an accuracy of about 0.001% (!).  Accuracy, namely signal settling, takes time.

So, an Audio ADC is typically 16-24 bits, and has an effective sampling rate of 44kHz to 96 kHz or more.  (keep in mind the ADC is sampling MUCH faster than this because of sigma-delta modulation).

A video ADC is typically 8-12 bits (sometimes 14b) and samples between 10 - 40 MHz.

An ADC in a Gb Ethernet chip would be more like 6 - 8 bits @ 125 MHz.

An ADC in a 10Gb Ethernet chip would be more like 6 - 8 bits @ 1.25 GHz.

An ADC for a DDR4 transceiver or a radar receiver may be more like 4 bits at 10 GHz.

And so on.  The reason there are so many ADCs is that there are so many places in the parameter space.  Do you care about noise?  It will cost you.  Do you care about power?  It will cost you.

A general-purpose ADC is a balance of different factors that has use in a variety of applications, but can't perform at extremes of speed or accuracy.