What is the difference between API and interface?

An API is nothing but “Application Programming Interface”.

API – it’s validating the record(s) and inserting directly into base tables. (if any error occurs, it’s just thrown an error at run time.)

Interface – Loads the data through interface table(s) and error-out record(s) histories' available in the same interface tables or provided error tables.

(The below image can help you understands easier way.)