PNG format is a Lossy compression scheme, TIF is non lossy, no compression. In real words, that means that png literally destroys parts of the image, while tif does not. They are comparable to the difference between jpg and bmp. Png, in most (but not all) cases, is set up to blend pixels as it compresses, so you can get some color shifts int he process. Like any good compression scheme, it does its best to remove information that isn't critical and that usually wouldn't be noticed. There is a great deal of subjective decisions making that goes into that, and that's why some people prefer a lossless image with alpha channel such as tiff to the png format. Tif's are large becuase they don't throw any information away.

thou and I, my friend, can, in the most flunkey world, make, each of us, one non-flunkey, one hero, if we like: that will be two heroes to begin with. (Carlyle)