Basically you have to kinds of APIs, the ones that use SOAP and the ones that use REST. And the two acronyms stands for different types of ways to receive and respond the applications requests. A RESTful backend service is a backend service that adheres to the REST architectural style .
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RESTful api, and web services in general, are a way to abstract back ends from front end developpers . It allows front-end developpers to do their interfaces without the need to code any server-side logic. Web services contain all the business logic.
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