In Italian, it is not at all the same. It is normal in Italian to say the equivalent of "Yesterday, I have eaten a pizza", but not in English. My way of looking at it is that in English, the meaning of "have" never ever changes, whereas in other languages it sometimes becomes something special, a "helping verb". In English, "have" always indicates possession. When you say "I have eaten a pizza" you really are saying that you now possess something, and the something that you now possess is the experience of eating a pizza.