• It's a subjective difference, but a plot of land is usually larger (like something you would build a house on, or a farm). A patch is smaller (like something you would turn into a garden; the common expression is "a patch of grass.")
    A "lawn" would be a controled area, cut to a length and probably in a shape (square, round, emu-shaped or anything else for that matter). "a patch of grass" would be a small area of grass, normally this would not be a lawn.