Software engineering management can be defined as the application of management activities — planning, coordinating, measuring, monitoring, controlling, and reporting — to ensure that software products and software engineering services are delivered efficiently, effectively, and to the benefit of stakeholders.
— http://swebokwiki.org/Chapter_7:_Software_Engineering_Management
Source: SWEBOK
Software engineering is an engineering approach to software development. A practitioner, called a software engineer, applies the engineering design process to develop software.
The terms programmer and coder overlap software engineer, but they imply only the construction aspect of typical software engineer workload.
A software engineer applies a software development process, which involves defining, implementing, testing, managing, and maintaining software systems and, creating and modifying the development process.