Many people are unaware of the difference between these two set-ups. Even though both bikes carry only one "Drive Gear", the two have very different riding characteristics. Now, a single speed bike has a freewheel which is threaded onto the rear hub, this means the wheel can only be driven forwards and also it allows the rider to coast.
A Fixie or Fixed-Gear set-up has a single cog threaded onto the rear wheel hub, so whatever the rear wheels are doing, so is the pedals. This is because the cog has no freewheel action and therefore the rider cannot coast with this set-up, but the rider does have the option to pedal back wards.
Just a Brief summary of the set-ups.