I have been having a beginner issue that I cannot seem to find the answer for. I am following a tutorial on YouTube and my image has a way lower resolution and is so much more jagged both in viewport and renders.
Looks fine to me, but you can raise the Viewport sampling value (see Render context menu, right side of each of your images) to improve the quality of the viewport render. Of course, this will cost you performance, so don't go crazy. If you just care about Renders, raise the sampling value for Render. 64 is very low for a lot of renders. Use 64 or fewer samples to make sure the composition is good then crank it up to around 500 for detailed scenes. For less detailed scenes, you can change the sampling to 100 and turn on Denoising in the View Layer context menu. Those are just my preferences--they work for me. But as a rule, render quality is proportional to the number of samples (up to a certain point, which is why I advise you shoot for 500 and not 1000)