[Alaska Mike]

Quoted from Bike Radar

Shimano derailleur compatibility

Older generation 8- and 9-speed Shimano mountain bike and road kit is mostly inter-compatible since until the introduction of Dyna-sys on 10-speed mountain bike groupsets, they both used the same cable pull ratio.

This means that you can use an 8 -or 9-speed mountain bike derailleur with road shifters or vice versa.

This lowly 9-speed, Deore mech is compatible with nearly two decades worth of drivetrains
This lowly 9-speed, Deore mech is compatible with nearly two decades worth of drivetrains

The only exception is pre-1997, 9-speed Dura-Ace gear which won’t play nicely with anything as it uses a totally different cable pull ratio.

Although it initially doesn’t appear to be the case, the situation is a bit more clear with the newest generation of both Shimano road and mountain bike components. Bear with us...
Shimano road bike derailleur compatibility

All 11-speed Shimano road components are inter-compatible — you could for example use a Dura-Ace 9000 derailleur with a pair of 105 5800 shifters
All 10-speed road components (except Tiagra 4700, see below) are inter-compatible — you could for example use an old Ultegra 6600 derailleur with old, 105 5700 shifters
Current 9-speed road components are backwards compatible with older 9-speed road and mountain bike components, excluding the aforementioned exception

The only exception to the above rules is Tiagra 4700 (and the associated RS405 hydraulic shifters) which uses the same cable pull ratio as current generation, 11 speed road kit. This means you could for example use an 11 speed derailleur with 10 speed, 4700 shifters.