I wonder why sum types are named like that. They are not the sum of their possible states in a way that I would recognize, more like an exclusive-or or one of out many. At some point I came up with an explanation, but I forgot it again. If you need to explain why something is simple, it's not simple.

The number of valid options is the sum of the valid option for each variant. This is also why product types are called product types.

If you have a struct (product type) containing an 8 bit integer and a boolean, the struct has 512 possible states. 256 for the integer, times 2 for each value of the boolean.

If you have a sum type where one variant is an 8 bit integer, and the other is a boolean, you have 258 possible states. 256 for when it's an integer, and 2 for when it's a boolean.

Sum types add the options of each variant, product types multiply the options for each item in it.