I am a bit confused then to what is still troubling you?

A Bike with a coaster brake is not a "fixie." It is essentially a Single Speed with a coaster brake.

A fixed gear bike has a continually moving drivetrain when the pedals are in motion. You must use back-pressure to the pedal stroke to slow the pedal motion to come to a stop when not using brakes.

What else needs clarification. I thought the wiki did a good job