Spring rate is the amount of force it takes to compress the spring 1-inch and is expressed in lb/in for coils and leaf springs. Torsion bars are measured in ft/lbs of torque. The spring rate determines how much the spring will compress as the loading increases. Think spring stiffness. Spring rate does not change through the life of the spring but spring load will change.
Wheel rate is the spring rate actually measured at the wheel (or tire). For coils and leaf springs, wheel rate is usually lower than the true spring rate due to spring angle and control arm leverage that can effectively lessen the rate at the wheel. Wheel rate is measured in lb/in for all spring types.
Unsprung weight is the weight of the tires, wheels, knuckles, hubs, solid axles (basically any part of the vehicle not supported by the springs), and half the weight of the springs, shocks, control arms, and/or links.
Sprung weight is the weight of the body, chassis, drivetrain, tools, parts, and the other half of the total weight of the springs, shocks, control arms, and or links.