Software Engineering is “the application of a systematic, disciplined, quantifiable approach to the development, operation and maintenance of software, and the study of these approaches; that is, the application of engineering to software”. (IEEE)

TL;DR
Software engineering is the discipline of the systematic development, operation and maintenance of software.

Q. What's the difference between a programmer and a software engineer?

A programmer wites code.
A software engineer orchestrates the tasks of the programmer.

They aim to “deliver value to the customer”.

Links

Software Development Life Cycle
Software Development Approaches