No idea on the AXI Bus you're talking about, so can't make comparisons.

MMIO (Memory Mapped I/O) is essentially memory (Whenever RAM or ROM) from OTHER devices that is directly visible on the CPU Address Space. My understanding is that from the CPU side, MMIO is mostly transparent (Except for the massive increase in latency) because it gets used like if it was interacting with its own workspace with regular instructions like MOV.

What PCIe ReBAR changes is that before, you could only see a 256 MiB window onto the GPU VRAM, so there was an added overhead since the GPU may need to relocate things from inside that window somewhere else on its total VRAM (So yes, it may be interpreted as if what you see from the CPU side is just some kind of exchange buffer). I believe the best way to describe how it operates is comparing it to EMS (Expanded Memory) from the DOS days since it also worked with a similar, if not the same idea. You could only see a portion of the total memory from what was installed on the EMS card (A 128 KiB window located on the upper part of the 1 MiB address space from the 8086 CPU), so you had to switch which Page (Region) of the memory was visible, adding a lot of overhead and most likely requiring an additional buffer in main RAM to move data from one Page to another. However, since I have no knowledge if the GPUs really work like that I can't confirm. I never knew whenever the 256 MiB is "fixed" (You always see the same Region) or if you can decide which section of the VRAM to make visible.

Just to close the loop, AXI bus[1] refers to a very common implementation, in the gateware/verilog, of a MIMO.

[1] https://en.wikipedia.org/wiki/Advanced_eXtensible_Interface

It’s also similar to how mmap() on 32-bit systems maps files larger than 2GB.