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This document is meant to show the different reasons to choose either the API (https://wiki.openmrs.org/display/docs/API) or web services (https://wiki.openmrs.org/display/docs/Web+Services)
API
For the API the external application installs the API jar in their application and could connect to a single OpenMRS database if they had the proper credentials in their runtime properties file
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For an external application to get or put data into an OpenMRS instance via web services, you have to install the rest module (https://wiki.openmrs.org/display/docs/Webservices.rest+Module ) in the OpenMRS instances and then program the application to make the appropriate calls in json format over REST to the web services module.
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