Do the flight results I get from the API include the low cost airlines, or only the big full service carriers?

In most cases yes, low cost airlines do appear alongside the full service ones, but it helps to understand how they get there. Full service airlines are usually reached through the global distribution systems that agents have used for years. Many low cost carriers sit outside those systems and are connected directly instead, so whether a particular budget airline shows up in your results depends on which connections your supplier has switched on for your account.

Because of that difference, the two can behave quite differently once a customer picks a fare. A low cost fare often has to be paid for straight away rather than held, it may come with fewer things included, and changes or refunds can be tighter and sometimes handled only by the airline itself. Baggage and seats are usually sold as extras rather than being part of the fare, so the first price on the screen can look cheaper than what the trip really costs.

There is also the plain fact that not every budget airline is open to agents. A few of them sell only to the public and will not deal through agency channels at all, and no API can create a connection that the airline does not offer in the first place.

The sensible next step is to ask which airlines are actually live for your account on the routes you sell most, then run a few test searches on those routes and compare the results with the airline's own site so you know exactly where the gaps are.