Are all the 2 amp Chargers are "Quick Chargers"?
All 2A chargers are not quick chargers and all quick chargers are not necessarily 2A (Qualcomm Quick Charge 3.0 is 3.2 V)


USB standard 3.0 in   lays down standards of 10 W: 5 V, 2 A  for smartphones and tablets 
Power = Voltage multiplied by Current and this equation determines charging speed. When you use a 2A charger instead of 1A charger, charging speed increases . You can
calculate the charging time required using the Battery Charge Time Calculator ( choose efficiency of charging at 90 % if your battery is not too old ). Your device is probably supplied 2A charger since the battery is big and charging with 1A would take long. You can plug in the values in the calculator and see for yourself
Quick charging / fast charging of entirely different.  Basic principle is to increase the power supplied in charging by increasing power, either by increasing voltage or current or both. See this for more details How does fast-charge work?