The meaning is very much the some. In my experience people will say "I have heard" in reference to something that is not a simple and factual reference but rather a reference to opinions, view, scientific theories, etc. Things that are open for discussion and consideration. So I would say, "I heard Jenny baked a pie". No big deal. But I would say "I have heard that all human life originated in South Africa." Well, that's up for debate.

Antuan has given you a couple of good examples to answer the 'How' part of your question. Now here's the "Why" part of your answer: We use the Past Simple - "I heard" - to refer to a specific event at a specific finished point in time. When we say, for example, "I heard Jenny baked a pie", you're referring to the moment when you found out about Jenny's pie. The time period ( let's say " an hour ago" ) is finished, and the conversation is finished. That's why we use the Past Simple. You might say it in the following context : "I heard that Jenny baked a pie ( when I spoke to Bill on Whatsapp an hour ago)". We use the Present Perfect - "I have heard" - to refer to a general period of time up to now. We also often use it to talk about our life experiences so far, without specifying when exactly these events occurred. When you say "I have heard that all human life started in South Africa", you may be talking about several different occasions on which you read or heard about this idea, perhaps from various different sources. So you might say it in the following context: "I've heard many different ideas about the origin of humans. I've heard the idea that we originated in Mesopotamia, and I've also heard that we originated in Africa." You aren't focusing on a particular event at a specific time: you're just talking about your experience of hearing about this topic in your life up to now. That's why we use the Present Perfect.

By the way, your question should be this: "What is the difference between 'I heard' and 'I have heard'?"