Depending on the coffee shop, this is either a cappuccino based drink with some chocolate in it (maybe made with chocolate milk), or it's what other shops call a mocha. Both are made from espresso.
The cappuccino one comes in the same sized cup and has the same milk foam a cappuccino does. The mocha kind is more like hot chocolate with espresso it it; larger mug, sometimes topped with whipped cream and chocolate sprinkles.
Another source of confusion can be large coffee chains, such as Tim Hortons, insisting that an Iced Cappuchino or Iced Mochaccino is like a slurpee but creamier, while small shop who know make an Iced Cappuccino by pouring normal cappuccino over ice.