In Koine Greek, what is the difference between the perfect tense and the aorist tense?

Ancient Greek has four past tenses; Modern Greek has two, and an auxiliary formation for the other two. The tenses differ in aspect.

The imperfect emphasises that the past action was ongoing or continuous.

The perfect emphasises that the past action is now complete. The main reason for doing that is, as Konstantinos Konstantinides points out, because the results of that past action are still relevant now.

The pluperfect emphasises that the past action was already complete before something else happened.

The last tense is the aorist; in other languages, it is usually called the simple past. It doesn’t indicate whether the action is or was complete or ongoing. In fact, aorist is the Greek word for “indefinite”. It simply states the action happened in the past, and it acts as a default past tense.

If you have to infer an aspect for the aorist, you can infer (by default) that the action is complete, but unlike the perfect, the results of the action are not with us now: it is, so to speak, history.