jBPM5 is a framework that you can use to create applications that execute business processes defined in BPMN2 notation (this is the ultra-simplified definition :) ). So, jbpm API are the classes and methods that allow you to compile a process, start a process and interact withit (signal events or complete tasks).
jbpm-console is a web application that lets you manage and interacto with processes in a visual way. Under the hood, jbpm-console uses jbpm API.
If you are planning to use jbpm-console, then I would suggest you to implement your simplified web ui using REST API: http://docs.jboss.org/jbpm/v5.2/userguide/ch11.html#d0e3556
The REST API implementation in jbpm-console will internally use jbpm API to execute the commands.
Best REgards,