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They are very similar but I can't understand which one is the correct one to use.1 answer
By saying past simple and present perfect I presume you meant the passato remoto and the passato prossimo.
The difference is quite simple thankfully. the first one is not actually really used in the spoken language and even in the written unless you are writing a novel or some formal document or in news. The passato remoto (past simple) is used for past actions and using it while talking to someone is a bad idea.
The second one is the main past tense we use for expressing the past in most cases (together with the imperfetto).
Let me give you some examples.
Marco andò a casa. Marco went home.
This sounds like a sentence of a novel.
Marco è andato a casa. Marco has gone home.
This sounds like everyone would say it in everyday life.
In English you would rather use the first one but in Italian it's the opposite.