Per commentary by the OP, apparently what's needed in the answers here is a catalog.
American Red Pepper Flakes: Dried and crumbled flakes of cayenne peppers per other answers. Used extensively in general American cuisine as well as Italian-American cuisine. In the US, often substituted for harder to find pepper flakes that would be more culturally appropriate to the dish (such as those below).
On the occasions that Italians in Italy use "red pepper flakes", they are more likely to be Calabrian Peperoncino.
Turkish/Syrian/Lebanese Red Pepper Flakes Most of the time the crumbled flakes of dried "Aleppo Pepper" (pul biber). However, the civil war in Syria has restricted supplies of this pepper, so often what is labeled "Aleppo Pepper" is actually Marash Pepper or Antebi pepper instead -- which are both tasty but hotter than Aleppo, so adjust accordingly. The Turkish also use Urfa Pepper flakes, so if your recipe is Turkish and doesn't specify, it could be any of these.
Korean Red Pepper Flakes: gochugaru, the flakes of the Korean red pepper, a medium hot pepper. Used liberally throughout Korean cooking, in flake, powder, and fermented paste form. Possible the best substitute for Aleppo pepper if you're completely unable to find any Turkish/Syrian pepper varieties.
Mexican Red Pepper Flakes: varies, and you really want to read the label. Frequently crumbled chile de arbol, which are screamingly spicy. But ... could also be flaked chipotles (dark and smoked) or ancho chile (medium-hot), or other peppers. Take nothing for granted. Ancho Chile is also the main chile used for American "chile powder".
Chinese Red Pepper Flakes: usually flakes of the Sichuan "jin tao" pepper, used in Sichuan and Hunan cuisine, but could be a different pepper if the recipe is from a different region. Spicy and fruity.
Indian or Thai Red Pepper Flakes: these two cuisines very rarely use peppers in flake form; they generally use whole peppers instead. As such, any mention of "pepper flakes" in an English-language Indian or Thai dish is likely to be a substitution for whole peppers, and as such probably means the American cayenne flakes. However, various Indian peppers are available in flake form in the US, so could also mean those.
Undoubtedly there are other cuisines that use something described as "red pepper flakes", but this should give you an idea of the breadth of ingredients that label could apply to. You need to depend on context -- or, ideally, a glossary in the cookbook -- to figure out what's actually meant.
Your case is an example of the problem with American-Ethnic recipes. A recipe for Turkish Meatballs written by an American could mean Aleppo pepper, but could also have been adjusted to use the common cayenne pepper flakes. Without specific information in the recipe, there's no way to know -- but it's also hard to fail by using Aleppo pepper.