When I dine out for Indian cuisine, I prefer to order my food hot on the mild/medium/hot/spicy scale. This question is two-fold.
Several of the spices in 'indian' cooking will impart a sense of heat - ginger, peppercorns etc - but the single ingredient used in restaurants & take-aways as a last-minute heat booster is Cayenne chilli powder. The basic curry sauce will be mild, so none is added if you order mild. The hotter you order it, the more they add. They will use many other last minute additions to make your specific curry 'type', but the heat is chilli powder.
The upside of cayenne is it doesn't add a lot of flavour, mainly just heat, & it doesn't need to be cooked in for hours to give the heat boost. It will come in a couple of minutes. You can even mix it in at the table, if you're feeling the need of a booster.
'Cayenne' is not one specific chilli, it is a type of chilli; often mis-labelled & sometimes to avoid the mis-labelling is just called 'hot chilli powder' [though in the UK you sometimes need to check the ingredients list to make sure it's not actually a mix for chilli con carne].
Though it's a specific a type of red finger chilli, the name has kind of been used to cover many similar chillies, and the powders you buy are often blends of many similar types. Getting 'exactly cayenne' isn't actually important. Very few people will ever be able to tell the difference.
Apart from the red chilli powder made from dried red (ripe) chillies (mentioned in the other answer), green chillies are added to the curry during some stage of cooking. There are a variety of green chillies which have different levels of heat/spiciness.
Restaurants in India often place a couple of raw green chillies on the plate to directly chew on. Sometimes these chillies may be "pickled" in salt crystals.
