API and Protocols
An API can also be an implementation of a protocol.
In general the difference between an API and a protocol is that the protocol defines a standard way to exchange requests and responses based on a common transport and agreeing on a data/message exchange format, while an API (not implementing a protocol) is usually implemented as a library to be used directly: hence there can be no transport involved (no information physically transferred from/to some remote machine), but rather only simple information exchange via function calls (local to the machine where the elaboration takes place) and data is exchanged in formats expressed in a specific language.
When an API implements a protocol it can be based on proxy methods for remote invocations that underneath rely on the communication protocol. The role of the API can be exactly to hide the detail of the transport protocol. E.g.: RMI is an API that implements the JRMP protocol or the IIOP as RMI-IIOP.
Protocols are usually shared between different technologies (system based on given computer programming languages in a given operating system) and usually allow the different technologies to exchange information, acting as an abstraction/mediation level between the two worlds. APIs are usually specific to a given technology: hence the APIs of a given language cannot be used in other languages, unless the function calls are wrapped with specific adaptation libraries.
Read more about this topic: API, Detailed Explanation