At their core, web APIs are simple HTTP client-server environments. A request comes in over HTTP and a response goes out. To standardize things a bit more, a couple of protocols have been developed, and many APIs follow one or the other to process requests. This is by no means an exhaustive list, but it is likely what you'll encounter in the wild:
Representational State Transfer (REST)
Simple Object Access Protocol (SOAP)
There are certainly other types of protocols that APIs can use, but while their protocols differ, the majority of the same security challenges remain. The most popular protocols are RESTful APIs, followed by SOAP APIs.
SOAP was developed by Microsoft because Distributed Component Object Model (DCOM) is a binary protocol, which makes communication over the internet a bit more complicated. SOAP leverages XML instead, a more structured and human-readable language, to exchange messages between the client and the server.