A Tone Match is a hi-resolution EQ, very much akin to an IR, but using a longer sample time (e.g. or maybe multiple samples taken over time?) in order to make input audio A sound like the sampled clip, given a reasonably close amp is already there.
So a Tone Match (in a Tone Match block) created on the AxeFX II/III cannot be shared with an AX8 user since the AX8 does not have the Tone Match block, but a Tone Match block can be converted to a CAB block to share with an AX8 user to load and use.
That's my understanding.