Red Chile is a generic term for a mildly hot pepper, usually small in size.
When you see it in a recipe, the writer is usually calling for a red chile for the colour it will add to a dish, as well as for the general belief that red chiles have more zip to them than other chiles, which is not always true. How much zip you are adding depends on what kind of red chile you choose. If you are making a European recipe, such as Italian or Spanish, choose a very mild red chile.
The generally intent in calling for a red chile is for a chile about 1/4 the way up on the hotness (Scoville) scale. Generally, it would be called for in a more European or Europeanized recipe to add a little zing to it, while still enabling all diners to enjoy the dish.
You know you’re getting into a more serious Tex-Mex, Mexican or South American recipe if the actual red chile variety desired is mentioned by name (e.g. Habanero), and if more than one type of red chile is called for (e.g. New Mexico, plus Ancho.) Using different chiles “layers” the taste, making it more complex.