Most people think of only software programming when they think about software engineering. But software programming is only a part of software engineering. Software engineering includes every activity which is done so that a software product can be built. All software engineering activities start when a requirement for a software product arises. A project team is formed to design and build the software product. This project team consists of business analysts, software designers, software developers, software testers, database creators, project managers etc.
Project activities start when user software requirements are gathered by business analysts. From user software requirements, software requirement specifications are created in form of use cases. Use cases are then taken by the software designers to create software designs. Software designs consist of user interface designs, business logic design, database design etc. Once software designs are created then software developers start writing source code in a chosen programming language. The source code is compiled to create the machine code which is the software product. This product is tested to ensure that it has no defects. Finally this product is released so that users can use the software product.
You can see that a lot of activities take place right from software requirement gathering to software design creation to software development to software testing to software release. All these activities come under software engineering. All the software engineering activities are managed through software project management.
This can easily be seen that software engineering is a vast field.