MIDI is the Musical Instruments Digital Interface and is a 7 bit control protocol running at 31.25 Kbits per second. It has nothing to do with audio sampling and merely tells a receiving device note on/off, note number, channel, key velocity, pressure (after touch), pitch bend, modulation, program change and system exclusive parameter changes.
The mellotron was not pioneered by Robert Fripp; it is/was an instrument consisting of piano-like keys which trigger a tape loop each. Listen to Strawberry Fields by the Beatles (recorder recordings, confusingly) or Nights in White Satin by the Moody Blues (strings and female choir) or Phaedra by Tangerine Dream (more strings) to get a feel for it. Rough and gritty and lovely.
Audio sampling is the process of recording audio as discrete time domain events. In the case of analogue sampling a BBD (bucket brigade device) is used. It is similar to the CCD in your camera and typically will have 512 capacitors in a row with the audio signal recorded as an instantaneous level at the sample-and-hold input and passed from one cap to its neighbour until it arrives at two outputs in turn, allowing for interpolation by yet another cap with a resistor (low pass filter) to give a reconstituted signal. Quite noisy, but with a distinctive sound - think 1980s indie jangly guitar chorus ( Cocteau Twins).
Digital audio sampling (go and google Shannon, Nyquist) is the process of converting a signal into discrete numbers by use of an analogue to digital converter and then turning it back into an audio signal using a digital to analogue converter. The signal to noise ratio is governed by the resolution (number of bits) of the converters and a function of the sample rate, and the sample rate governs the bandwidth of the signal and also the signal to noise ratio.
The Fairlight CMI was the first commercially successful digital audio workstation - a device which allows for sampled and synthesised audio to be sequenced as music.
It's a big and beautiful subject and there is a lot of accurate material out there on the Interweb - use this post as a diving board.