Difference between an API and SDK

Piece of cake:

• an API is an interface. It's like the specification of the telephone system or the electrical wiring in your house. Anything* can use it as long as it knows how to interface. You can even buy off-the-shelf software to use a particular API, just as you can buy off the shelf telephone equipment or devices that plug into the AC wiring in your house.
• an SDK is implementation tooling. It's like a kit that allows** you to build something custom to hook up to the telephone system or electrical wiring.

*Anything can use an API. Some APIs have security provisions to require license keys, authentication, etc. which may prohibit complete use of the API in particular instances, but that's only because particular authentication/authorization steps fail. Any software that presents the right credentials (if required) can use the API.

**Technically, if an API is well-documented, you don't need an SDK to build your own software to use the API. But having an SDK generally makes the process much easier.

API is like the building blocks of some puzzling game that a child plays with to join blocks in different shapes and build something they can think of.

SDK, on the other hand, is a proper workshop where all of the development tools are available, rather than pre-shaped building blocks. In a workshop you have the actual tools and you are not limited to blocks, and can therefore make your own blocks, or can create something without any blocks to begin with.

coding without an SDK or API is like making everything from scratch without a workshop - you have to even make your own tools