What is the difference between pay and/or reward system in any company?

There is no universally applicable meaning attached to
these terms.

All the monetary and non monetary benefits the
employees get from their employees in return for their services are generally called
their compensation or reward for employment. The schemes or system used for determining
such rewards are called compensation or reward system.

The
total reward given to employee is classified in two categories. Monetary rewards and
other benefits. Monetary rewards are again divided in two parts. First is a fixed pay
part, which is a basic payment paid on the basis of a fixed time or piece rate. The
other is a variable pay, which is payment made based on performance in addition to the
fixed pay. The variable performance based payment are given under the names such as
incentives and commissions. Some companies describe the system used for all the monetary
payment as pay system. Other companies use the term only for the system of fixed pay
under the pay system and use include variable payment under separate system called by
various names like incentive system of commission
system.

Sometimes the term reward is also used for
recognition and special payments or benefits in kind given to employees for some special
achievement. For example employees with exceptionally good performance may receive
reward in form of paid holiday with family at some exotic tourist destination. Or a
salesman may be given special recognition in the form of an award called "best salesman
of the year", accompanied by some monetary payment.