Horizontal dropout vs track end. Both have slots you can slide the wheel axle in. Both slots are roughly horizontal. The difference is: the track drop was designed for track bikes, ie the bikes that are raced in the banked velodromes. They want a means of moving the wheel to adjust the chain tension (really I mean slack; a non-derailleur bike should never have tension on the chain save from your pedaling efforts). Track drops are truly horizontal so moving the wheel has no effect on bottom bracket height or pedal clearance. The slot is long so a racer can ride any cog he needs for an afternoon of racing without massing with his chain length. The slot opens to the back. Easy to make. A bit of a hassle pulling the wheel off. First you hafe to get the chaim off teh cog before you can continue. At the velodrome, where they do not allow dirt, chains stay clean and this isn't an issue. Nor is the time factor. Track races don't allow wheel changes for flats while the race is going.

Horizontal dropouts open to the front and have a slight angle so as you slide the wheel the distance to the rear brake pad doesn't change. Road dropouts evolved for road racing. Flats happen and are a part of the sport. There is a need to get wheels out quickly. Opening to the front speeds this up a lot. This is just as true for single speed and fix gear wheels as derailleur wheels.

Many horizontal dropouts (and most of the good ones) have adjusting screws. You can get your chain tension right once, then tighten those screws until they just hit the axle. Now when you flat while out for a ride, you don't even have to think about setting the chain slack. Just pull the wheel back until the left side hits that screw. Tighten the hub nut. "Rock" the wheel until the right side hits. Tighten the right nut. (You may have to do one more rock to the left.) Done. Jump on and ride.

Take a look at the fix gears and single speeds you see. Newer ones will be almost all track ends. Many of the older ones will be resurrected 1980s bikes with horizontal droputs. Track ends are "the thing". Shop employees will probably tell you you have to have them. Those of us who have been riding fixed for 3 and 4 decades have little use for them.

Hope thisx helps. And I hope the right bike falls into your hands!

Ben