Corn syrup is an ingredient with many uses in the baker's kitchen. It is one of a class of sugars called "invert" sugars, which remain liquid rather than crystallizing. It also helps prevent other sugars from crystallizing, which is one reason it's often added to candy and frosting. Another reason it's sometimes added to frosting is to thin the consistency slightly, making the frosting more spreadable.
Golden syrup is a sweetener that's popular in Britain and the Caribbean. It's often referred to in English cookbooks as "light treacle" to differentiate it from molasses, which is "dark treacle." It is a sugar syrup with a pleasant but neutral flavor. Golden syrup is slightly thicker and more viscous than clear corn syrup. They can be used interchangeably in frosting, but golden syrup will give a faintly golden color to white frosting.
Glucose is another form of invert sugar, one that's primarily used for industrial purposes. It is very thick and sticky and won't pour very readily. It's usually spooned from its container. Aside from industrial sweets, glucose is mainly used by home candy makers and cake decorators for its ability to prevent sugar from crystallizing. To use it in frosting, thin the glucose with a small amount of boiling water until it reaches a consistency similar to corn syrup.
Honey is the only major form of invert sugar that occurs naturally. It resists crystallization in its natural state right from the hive, and when it eventually does crystallize it can be liquefied by heating it for a few minutes until it melts. Honey can be used in frosting either to prevent crystallization or to thin it for easy spreading. Honey is slightly sweeter than corn syrup but can be directly substituted. Like golden syrup, it will color the frosting slightly, and it also adds its distinctive flavor.
It's possible to make a simple sugar syrup at home that can be used in place of light corn syrup or the other liquid sweeteners mentioned above. Simmer three cups of sugar in one cup of water along with a tablespoon of lemon juice. The sugar will dissolve completely after about ten minutes of simmering, forming a thick syrup. The combination of heat and acidity will change the sugar's molecular structure, turning it into an invert sugar like corn syrup. Let the syrup cool before you add it to your frosting, or it will melt the butter and ruin the frosting's texture.