AMB make the full timing systems, loops, decoders, and PT's, and is the most common timing system used in RC all over the world as far as I know.
MRT just make compatible transponders.
AMB transponders each have a single unique number stored in them.
MRT transponders have 1 main number, that is a clone of an AMB one that MRT themselves own I believe, and they make/sell many of their same few (I say few...it's probably quite a lot!) numbers to people. BUT...they also have a number of default backup numbers stored in them which you can change to to use should you be at a meeting and get a clash. Clashes are very very rare though from what I can gather!
If you own an AMB PT you can send it to MRT and they will make you clones of your AMB PT, meaning you can have as many PT's of the same number as you'd like.
The latest AMB PT's (code named 'Harry') have allegedly got a higher signal output than the previous AMB versions and the MRT's, and will in future allow you to have 'clones', which have an extra digit stored in them for each clone, meaning even your clones are actually unique as well, but this has not yet been released and the working details of this not yet known.
In practice the AMB's and MRT's all work perfectly well, the MRT's are cheaper than the AMB's.
AMB Harry's are available via BBK Software, MRT via MRT themselves, but their site seems to be pretty basic at the moment, and doesn't seem to have any links to buying from them?!?!?
Hope that helps
