We can use standard REST API to pull list of sObject records to External system from salesforce.
Please find below REST API to pull list of Account based on Name and Website
Production URL:
https://login.salesforce.com/services/data/v37.0/query?q=SELECT+Id,name+FROM+Account+WHERE+name='Sathish'+AND+website='www.sathishsfdc.wordpress.com'
Sandbox URL:
https://test.salesforce.com/services/data/v37.0/query?q=SELECT+Id,name+FROM+Account+WHERE+name='Sathish'+AND+website='www.sathishsfdc.wordpress.com'
Sathish SFDC 