My opinion is SIS (sometimes called ESD Emergency Shutdown System).
FGS send the shutdown command to SIS via hardwired.
If you have FGS cause and effect diagram, you find the detail.
> Who initiates the shutdown in-case of fire or release of dangerous gases?
> Is it the FGS or SIS?
It's depends on spec requirement and HAZOP study.
in case of that SIF scenario had been studied and SIL level assigned, you have to design with SIL.
However I believe "Shutdown" which you referred including many effects.
And if any of effects has been used final elements by SIF, they should controlled by SIS, it means anyway you have to send signal to SIS from FGS.
So it's better connect 1 output from FGS and make effect from SIS.
*Please note if gas detection and shutdown is defined as one of SIF, SIL calculation shall include GD,FGS,SIS,final elements all of them.
Do we practice to add FGS in SIL analysis as per IEC 61511? How we can achieve the safety if detector placement goes wrong?