I am going to take another stab at describing the difference.

As someone mentioned single speed generally refers to the types of bikes we all grew up with. You can stop pedaling and coast without your feet moving. If you had hand brakes, you could actually turn the pedals backwards with that click click click sound. If you had coaster brakes you would stop if you pedaled back, but you could still coast without moving your feet.

On a fixed gear the gear in the back is screwed tightly onto the axle with no freewheel mechanism. As someone mentioned if you pedal forward you go forward, if you pedal backward you can go backward. The main thing to keep in mind, and, to me, the most important implication to someone trying fixie for the first time, is that if the wheels are turning, the pedals and your feet on them, are turning. You cannot stop pedaling and coast. When you are coming to a stop you cannot coast. When you are starting off you can't just give a push on the pedals then pause as you settle onto the saddle. The first time I got on my fixed gear I gave a big push then stayed standing anticipating to coast for a second as I sat down. Doesn't happen. I almost got bucked off my steel bronco. So fixie riding has to be approached with a touch of respect.

Is fixed gear better? Each person have to figure that out. To me it gives a more direct feel to the cycling experience. You feel really connected to the bike, to the road, etc. It is kind of exhilarating. I alternate between a multi-geared bike and a fixie. Fixie is definitely fun.