A tarck bike is to a track bike what a modern Sport Utility Vehicle is to a Jeep CJ. One is designed for looks, while the other has a specific utility.
Track bikes are meant to go fast on a velodrome — an oval track with banked turns designed specifically for bicycle races. They have a single, fixed gear, no brakes, and a stiff geometry that favors acceleration over ride comfort. The venerable Bianchi Pista is your standard track bike, and is often the bike available as a rental at your local velodrome.
Tarck bikes aren’t necessarily true track bikes — they can start from track frames like the Pista, they can be conversions from other styles of bike frames, or they can even be designed as fixed/singlespeed “urban” bicycles complete with bling components, top tube pads, BMX grips, and brightly colored deep dish rims. Some outfit their bikes for trick riding with upgraded components — BMX bars, beefier forks, fatter tires and so on. I think you know the look.
“Tarck” used to be pronounced with a certain sardonic snarl, but these days tarck can be an affectionate shorthand for these kinds of bikes favored by young people all around the world. In the UK, I’m told they call this a “Hip Hop Slave Bike,” or HHSB, and usage is similar.