Hello Tim. I guess to try and put your mind at ease a little bit, in the fundamentals you’re getting introductions to notions and conceptualizations, you don’t really need to worry yet about getting exactly the same look as what’s on screen, usually there’s a bunch of things that goes on before a teacher hits record and right now they aren’t focusing on result/ goal oriented outcomes, otherwise they would explain every little thing. Right now the important thing is the knowledge, that you get to know the concepts and you can play around yourself in Blender. So in the meantime, you can relax the expectation of a goal oriented training, that comes in other courses where you’re aiming for an outcome.
In this case what you’re describing it’s probably that you have the denoise on, you can see it on your screenshot, the Denoise checkboxes are on for both the viewport and the render. You can disable those.