If you spend just a few minutes in front of any cheese case, you will probably be struck by how different the cheeses look.
They are of different sizes (from a 4 oz chèvre button to a 50 lb cheddar); different shapes (truncated pyramids, flat brie, spherical Mimolette), and also different colours (bright white fresh goat cheese, juicy red Red Leicester, golden Appalachian, and fudge-brown Gjetost).
The size and shape of the cheese, is normally determined by the mould or cloth used to hold the curd while the cheese's form is created, and the moulds are usually chosen to match the type of cheese being made.
You don't get tiny cheddar pyramids for a reason - cheddars just can't be made that way.
The colour of cheese is controlled by different factors, and the final colour of a cheese can be influenced by a mixture of one or all of these.
Cheese comes from milk. Milk comes from livestock, and livestock produce milk from their feed. The feed (be it grass or silage or other) can have a huge effect on the colour of the cheese. This happens through its own natural colour compounds (chromophores), or other components (fats).
b-carotene; Fresh grass and wild flowers contain colour compounds (chromophores), such as b-carotene, which have an orangey/yellowish tint. Cow's milk cheese, from cows who have a diet of lush fresh grass and flowers, will produce milk and cheese with a full, beautiful golden hue (see some Appalachian as an example). But b-carotene also gets broken down by sunlight, so hay-fed cows will have a more pale cheese, a cow's fed on no grass, well, white, white, white white.
Note the mention only of cow's milk? Sheep and goats break down the b-carotene in their stomachs, and none remains to colour the milk/cheese! Hence their generally whiter colours.
fat content; Milk's constituents, especially protein and fat, vary widely across the different breeds of cattle, sheep and goats (and a year's seasons). And fat can play a role in colouring cheese - high fat levels (which indicate a richness of milk and healthiness of cattle) will lend a yellowish hue. Think of 0% milk, and how grey and thin that looks, as compared to the rich yellowness of cream.
The colour of cheese can also be altered by external factors - us humans of course!
achiote & annatto; A high fat content and high levels of b-carotene indicate healthy, happy cows, and suggest a rich, full, wonderful cheese. Medieval cheese makers realised that by using a common, natural food colouring called annatto, they could fake a cheese to be from happy, healthy cows. Annatto comes from the seeds of the fruit of the Achiote tree in Central and South America - and it's a powerful colouring agent as you can tell from the picture! A few drops will easily colour a gallon of milk. Even today, large industrialised, supermarket cheese is coloured yellow/orange with annatto, to conceal the quality of their milk.