I am using single publication and two Business process types(Staging, Live)
I have setup 2 deployer, 2 discovery service for staging and for live.

My issue is when I run discovery service update (java -jar .\discovery-registration.jar update) for staging, The published pages from both of the target go to staging.
When I run discovery service update (java -jar .\discovery-registration.jar update) for live, The published pages from both of the target go to live.

I have checked the config setting of deployer/discovery both have their correct path/port set for staging and Live. 

Is there anything else I can check?

Thank you in advance