All gold is yellow - there is no such thing as red, pink or rose gold but there are gold alloys which appear rose, red, or pink.
Gold itself is a yellow but too soft to be used for general purposes in its pure form - so it's mixed with other metals to produce an alloy mixture of two or more metals. Most people prefer the color of gold jewelery close to pure gold - so most jewelery has been made using yellow gold alloys. Most gold alloys are a mixture of gold, copper and silver - small amounts of other materials are also added to provide special characteristics such as - nickel, zinc, and palladium - common components of white gold alloys.
Rose, Red and Pink Gold colored alloys are very simple to produce by increasing the proportion of copper in the mix. To maintain the correct % of gold in the alloy, usually means decreasing the silver content - and save cost - as copper is less expensive than silver. The difference between red, rose, and pink golds is only the name.
Only two metallic elements are not silver in color. Gold - yellow, and copper - red. By adjusting the proportions of gold, silver and copper, it's possible to vary the color from very pale yellow - "green" gold, to a deep red, or to a deep gold.