I have experience with MTM, not bespoke, but my understanding is as follows:
Bespoke: The tailor starts with your measurements, as opposed to a stock pattern. After taking exhaustive measurements, and allowing you to specify every detail of the suit, construction begins. Along the way, there will be multiple fittings so that adjustments may be made between the initial measurements and the final product.
MTM: A MTM suit is based largely on a stock pattern. When I had a MTM done, I tried on a number of sizes and cuts, found the cut/size of jacket and pants that worked best, and that was the baseline for the suit. Measurements were taken and adjustments specified (take in a bit here, shorten there, etc.). MTM also allows many details to be specified (such as: 2 or 3 button, slanted pockets, pocket flaps or none, ticket pocket, peak or notch lapel, flat-front or pleated trousers, belt loops, side tabs or just brace buttons)
It seems there's another category, MTO (made to order), which just lets you pick from stock patterns and fabrics, but allows more mix-and-match than buying OTR.