MPO, or "multi-fiber push on", is defined as such by International Electrotechnical Commision (IEC) and Telecommunications Industry Association/Electronic Industries Alliance (TIA/EIA) standards.
Specifically the IEC 61754-7 which defines the standard interface dimensions for the MPO family of connectors and the FOCIS 5 which presents the intermateablility standard for connectors with the designation of MPO.
MTP is a trademarked name used to describe a brand of MPO connectors, MTP is fully compliant with the above MPO specific standards, much like the difference between Kleenex® and facial tissue.
In conclusion MTP connectors are created using a patented process while MPO connectors are created using a different, always advancing process. All MTP parts are MPO but not all MPO are MTP and while there are slight differences in the branded MTP connectors they are still MPO connectors.