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