For a more detailed explanation, please read the article at believermag.com that I already gave a link to.
The Mellotron uses pieces of tape to record samples of sounds that only last for 8 seconds. The Birotron uses recordings on 8 track tape cartridges, so it holds the sound indefinitely when a key is pressed, allowing an endless loop for notes with infinite sustain. Also, the keyboard can be played quicker and therefore faster than that of the Mellotron.
Both instruments use samples of real instruments/voices to reproduce sounds.
The Mellotron was initially a rip-off of the Chamberlin.
In 1962, Bill Franson, Harry Chamberlin's salesman absconded to England with 2 Chamberlins, relabelling them 'Franson' and getting an engineering company, Bradmatic Ltd to manufacture the playback heads. Bradmatic Ltd eventually became Streetly Electronics.
It's a long story. Read it all here:
https://en.wikipedia.org/wiki/Chamberlin
