API is always SDK, SDK is NOT always API

Application Programming Interface (API) is a set of operations that a developer can use to access the backend of a server. You use the API by calling it from your device to the Cloud (a bunch of servers connected to the Internet) running the service
- Networked API -
- Non-Networked API -
Software Development Kit (SDK) is a group of tools, including pieces of code, that gets embedded into a service. The SDK contains APIs and so, it calls on the API when necessary to execute tasks. The result is the developer calls the SDK locally and the SDK calls the API remotely

API Types

API Types	Description
Network Level	Network-Level API (synonymous to OSI's application-layer protocols) refers to any network protocol used to exchange data between participating parties. These are used to build Application-Level APIs and usually follows an API Design Pattern
Application Level	JavaScript - Native - V8 Engine - Web/Browser APIs - client-side application-level APIs built in to browsers API - 3ʳᵈ Party - application-level APIs to integrate within a broader application
Language Type	Language-Dependent API - only available in one programming language Language-Independent API - not restricted to one programming language

API Other