As briefly as it can be described......

A normal Internally Wastegated Turbo has 2 outlets. One is that main Turbine outlet, the other is the Wastegate. The Wastegate has a 'Flap' which is controlled by the Actuator. So, the Actuator holds the Wastegate flap closed until the pressure in the Boost system reaches a certain level controlled by the 'Pre-load' and Spring rate on the Actuator, where is allows the Wastegate to be blown open, thereby bleeding off excess boost pressure. This allows the boost level to be controlled.

Normally these 2 outlets vent into one exhaust, which goes through the normal silencer system and all comes out the back of the car.

On an internally 'gated turbo, you can separate the Turbine outlet from the Wastegate using a special divider and direct the Wastegate gasses down a separate pipe. This basically takes the strain off the exhaust, sending a proportion of the gasses elsewhere allowing the exhaust to be more efficient.

Normally people chose to have an unsilenced Screamer pipe that vents either under or out the side of the car. You can, however, add a Silencer or direct the Screamer pipe back into the exhaust further down the pipe. The main point is that the first few inches of exhaust are most critical as it normally contains a bend or two, so after this, you can normally get away with putting the pipe back into the exhaust.

With an Externally 'Gated turbo, you have to run a Screamer Pipe, although you do have the option still of taking the above measures to make it more bearable.

Hope this helps!!