Singapore is unique .. in SIN except for T4, incoming and outgoing pax are co-mingled. So unless you are flying out of T4 you just go to your departure gate when you arrive in Singapore, co-mingling with arriving and departing pax on the same level, even using the train if necessary between terminals (except for T4).

Most airports do it the way BKK does it, incoming international pax are sent to the arrivals level, isolated from the departures level and departing pax. The transfer counter allows you to get a boarding pass for your connecting flight (you can't use mobile BP at the transfer security, I believe) and use the transfer security to stay airside, not cross the border into Thailand and go back up to the departures level to catch your flight leaving BKK.

-David