In naming the parts of a PS, we talk about long-term memory (the rulebase) and short-term or working memory (the data). The rules consist of a condition and an action. The action is sometimes called a conclusion. Sometimes the rules are called productions.
The inference engine is often called the production-system interpreter.
Production systems work by forward-chaining. As discussed last week, this is a kind of inference which works forward from data to new data. A piece of data comes into working memory. If it matches a rule, the inference engine will fire that rule and perform its action. This action will most commonly add some more data to memory; in turn, that may trigger more rules. It's also possible for actions to delete data from memory, initiate motor commands, and even add new rules to the rulebase. See last week's notes.
The user interface in a PS is usually trivial, designed with few frills to give the researcher a view of what's going on inside. Whereas the LTM and STM are intended to correspond to functional parts of the mind, the user-interface obviously is not.