Very briefly, Inferno and Plan 9 kernels are similar, having common ancestry. Application programs on Inferno must be written in Limbo; it's the only language supported. Application programs on Plan 9 are usually written in C. Both systems use essentially 9P2000 as their network filesystem protocol.
If you want to write in Limbo, you have to run Inferno, but you can run Inferno on (l)unix, Windows or Plan 9. If you want to write applications in C, you can't use Inferno.
