Customers’ loyalty. Online

Answering questions we get in our support service from online businesses we sometimes see the difference in terminology we use.
Indeed, certain phrases like «consumer loyalty, customer retention, loyalty programs» are seldom to hear from web sites owners. More often they mention «bonuses, prizes, rewards, etc».
We hope that all of this will not cause a muddle  and problems in understanding what our product can do. All the functionality of  «PointLoyalty Manager» can be described as follows:
-   You create rules for rewarding your customers (loyalty program, prizes scheme, etc)
-    Submit information about your customers actions (purchases, clicks, messages, …)
All the terminology questions are secondary.