In your opinion what's the difference between the two? In my opinion both terms are frequently used interchangeably in the workplace.
But I'd like to consider myself as an engineer, because although I don't consider myself to be good at it, I think I cares about the software that I worked on, its interaction with other services, the big picture, and different kinds of small optimizations.
I mean, what is even engineering?
Well, if I remember my software engineering prof correctly, software engineering is mostly about bringing an engineering mindset to software development. You wouldn't just slapdash an airplane together in a weekend and shove it out on the runway. There's a process for making sure we don't kill people with deadly flying contraptions.
Software engineering is that same idea applied to software systems. There is a process for making sure we do our job without causing undo harm. You wouldn't want to just slapdash together something that has to be HIPAA compliant and has to meet other security regulations. You plan. You test. You revise. You ensure the product doesn't publish the sensitive medical records of every patient on the front page before it ends up in production. That is the work of a software engineer.
I really like this answer, because now I'm confident that I'm at least acting as an engineer. Thanks!
To build upon this, we need to keep in mind that at least in some jurisdictions the role of a certified engineer is only required in projects with relevant size, and the responsibility of that engineer is to ensure the project complies with all requirements and therefore be held responsible for any mishap. This means that it's perfectly fine if non-engineers work independently on complex tasks, provided that an engineer attests that their output is fine and takes responsibility in case it isn't and it causes problems.