The reason why we see the moon and sun to be similarly sized even though the sun is much larger is simply due to the distance of each of these bodies from us. The sun is very large, having a radius of almost 700,000 km. The moon, on the other hand, has a radius of about 1740 km. However, the sun is also farther away from Earth, being situated at a distance of about 150 million km, as compared to moon (which is only about 400,000 km away from us). If we do simple calculations, we can see that the ratios of distances to sizes for the sun and the moon are relatively similar. We always see a distant object as being small, while a nearby object looks big (in comparison). In simpler terms, put a tomato on the table a foot away from you and look at it. Now walk back 10 steps and look at it again. You will notice that it appears much smaller. This is also the case with the sun and moon.
Hope this helps.