How and why the appearance of the moon changes to an observer on earth?
Apart from the phases of the moon, already answered, the other difference you may be refering to is how the Moon appears to change size, ie near the horizon it looks bigger. An optical illusion due to our having nearer objects to compare it to- if you hold out a pencil at arms length and use it and your thumb to measure the apparent diameter of the seemingly huge “harvest” type of moon, then do the same with a bright “high-up” moon , they will be the same.
