A coder is somebody who writes code. Engineering is much broader discipline than just writing the code - it means writing it well, writing it to be concise, readable, maintainable, standards-compliant, specification-compliant, reliable, well-performing, possibly scalable, user-friendly and everything else that what is essentially a robust machine needs to be. In addition, software engineers can specialise in development, testing, design/architecture, performance, UI and probably many other things I can't think of right now.
What I'm saying is that making software good is hard. It takes a lot of different skills in addition to mere coding. Actually writing the code - pressing buttons on a computer to enter text into an editor - is one stage in a long process, and all of these stages are as important as each other.
Some of these are skills which you probably have! So calling yourself a mere coder is underselling yourself.