Coder isn’t a professional title. Software engineer and engineer are very broad of a term, because they can cover alot of work that’s not directly coding software. Not all programmers write software code, some just ‘program’ software that’s already written.
So i think developer is the best term for someone that ‘develops’ and write software code for a living. Or even software developer, those terms are interchangable.
The_Picard_Maneuver