Almost:
Technically device drivers implement, or provide expected functions, for an interface (which just an API, see below, or function specification), the interface being I/O and power management functions. Device drivers are a "layer."
Application binary interface, or ABI, refers to how function and system calls work on the assembler level. ABI answers the question: I am a function, how do I get my parameters (form the stack? from registers?, etc.) Two binaries that are obeying the same ABI standard can use, or call, each others functions.
Application programming interface is more likely what you mean. APIs are the well-defined functions, including function name, required parameters, and a detailed specification of what the function does, that allow programmers to take advantage of services offered by another binary. ABI is just concerned with "linkage" and not defining what anything specifically is trying to accomplish.