"Pay" is the agreed upon or contractual salary or wage for a given position, based on qualifications and experience in the position. It is more or less guaranteed each pay period, and as long as the person does well enough to keep the job, does not go down.
"Reward" or what is more commonly referred to as "incentive" happens more commonly when people receive a commission for sales or profit-sharing for the employees of a company. It can also include the year-end bonuses awarded when a department, individual or company does well.
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.