Substituting oil in baking?
Peanut and canola are vegetable oils. Vegetable oil is a catch-all term, it's not asking for a product labelled "vegetable oil" although you can buy it in the store. Oils labelled vegetable oil are blends and can be any proportion of things like canola (rapeseed), peanut, corn, sunflower, etc. Just don't use Olive oil, it is a vegetable oil but it won't be good for cakes!

Different vegetable oils will give different properties although most will give you about the same result. Canola is flavorless and relatively light while peanut is a bit richer and, well, peanut-y. The differences in your cake will be subtle, however.