We know that 1000BASE-LX transceivers can be used over multimode fiber, and should be able to reach distances of 550 m in addition to the usual 10 km over single mode fiber. 10GBASE-LR transceivers have the same 10 km rated distance over single mode, but I've seen no mention of using them over multimode, even for short distances.
What happens in practice with 10GBASE-LR over multimode, can it work at all? Is the difference in MMF performance between 1000BASE-LX and 10GBASE-LR just about the speed, or is there some other factor involved?
Then there is 10GBASE-LRM, which should work over 220 m of multimode fiber, even ancient OM1 fibers. But it's rated for only 300 m over single mode fiber. What does LRM do differently from LR to work better over multimode but so much worse over single mode?
(The stated link distances are from the Cisco SFP and SFP+ transceiver datasheets.)
10GBASE-LR can also be used over multi-mode fiber but due to lacking specification, there's no defined reach. I wouldn't recommend it for production because if a transceiver fails another one might not work the same.
Multi-mode fiber suffers from modal dispersion and is usually specified for a certain modal bandwidth, e.g. OM3 = 2000 MHz·km for 1300 nm (L). Therefore, the higher the transmitted frequency / data rate, the shorter the reach. This is why you need OM4 (3500 MHz·km @ 850nm) to reach 400 m with 10GBASE-SR while OM2 (500 MHz·km @ 850 nm) is fine for 550 m with 1000BASE-SX, both using the same 850 nm wavelength (S).
10GBASE-LRM uses lower transmitter power/receiver sensitivity and has little SMF reach. Additionally, its transmitter is designed for lighting MMF and the signal loses a great deal of power when coupled with SMF. While conditioning from SMF to the MMF can be done with (theoretically) no loss/attenuation, conditioning from MMF to SMF leaves only the 0-1 mode, resulting in significant attenuation.
The fundamental difference between SMF and MMF transceivers is how the light gets into and out of the fiber. Going from SMF to MMF can be achieved with little attenuation in theory but going from MMF to SMF, a severe signal power loss is unavoidable: all but one of the intermixed modes are lost and additionally the 'overfilled launch' causes another significant power drop.