From my experience, developer and software engineer are interchangeable titles, so it would make sense that you'd be doing development work if your title is software engineer.
A designer focuses on the product's overall design from how it functions to how it looks.
The difference between software engineer/developer and designer does matter, as most people and companies you talk to will have wildly different ideas of what you do depending on which you say you are. If you do both, then explicitly say so.
From my experience, developer and software engineer are interchangeable titles, so it would make sense that you'd be doing development work if your title is software engineer.
A designer focuses on the product's overall design from how it functions to how it looks.
The difference between software engineer/developer and designer does matter, as most people and companies you talk to will have wildly different ideas of what you do depending on which you say you are. If you do both, then explicitly say so.