The term "ground red pepper" is ambiguous in English. Things sold under that name in the US have a wide range of heats, and likely are made from multiple varieties of peppers, though I'd say they're more commonly hot things like cayenne, or other varieties with somewhat less heat.
That said, don't worry about it too much in these cases. Anything from mild paprika to cayenne would likely fit within what the authors meant, and you're not going to harm a recipe by increasing or decreasing the heat, or by using a chile powder with a slightly different flavor. Just use something (or a blend) that provides the heat level you want, and you'll be fine.