Does increasing the number of samples and increasing the resolution of a render affect the quality in the same way?
Because I've usually kept my resolution high and the number of samples fairly low.
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Sample size affects the amount of rays casted from your camera. Low sample size yields a lower quality image but a faster render time.
Your image resolution is the canvas size of your image. Image quality depends on the resolution of the display which you view the image.
For example if you have a 1920x1080 monitor and you render your image in 3840x2160; your display interpolates every 4 pixel in to 1. That might give you the impression of a higher quality image but it'll be blurry and/or noisy. If you really want to get a high quality image, you have to sample the pixels more so you'll get more accurate data on that pixels information. You will get a better result on reasonably lower resolution but high sample count render.